A198715 -id:A198715

A207868

T(n,k)=Number of n X k nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to any horizontal or vertical neighbor (colorings ignoring permutations of colors).

+10
19

1, 1, 1, 2, 4, 2, 5, 34, 34, 5, 15, 500, 2052, 500, 15, 52, 10900, 278982, 278982, 10900, 52, 203, 322768, 68162042, 455546040, 68162042, 322768, 203, 877, 12297768, 26419793726, 1625686993918, 1625686993918, 26419793726, 12297768, 877

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,4

COMMENTS

Table starts

...1.........1..............2.................5.................15

...1.........4.............34...............500..............10900

...2........34...........2052............278982...........68162042

...5.......500.........278982.........455546040......1625686993918

..15.....10900.......68162042.....1625686993918.103204230192540988

..52....322768....26419793726.10764437129618296

.203..12297768.15002771641712

.877.580849872

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..231 (terms 1..49 from R. H. Hardin)

Eric Weisstein's World of Mathematics, Grid Graph.

Eric Weisstein's World of Mathematics, Vertex Coloring.

Wikipedia, Graph Coloring.

EXAMPLE

Some solutions for n=5 k=3

..0..1..0....0..1..2....0..1..0....0..1..0....0..1..2....0..1..0....0..1..0

..1..0..1....1..0..3....1..0..1....1..0..1....1..2..0....1..0..1....1..0..1

..0..1..0....0..1..0....0..1..0....2..1..0....0..1..2....0..2..3....0..1..2

..1..0..1....1..0..1....1..0..1....0..2..3....1..0..1....1..0..1....1..0..1

..0..1..0....0..1..0....2..1..0....1..3..0....2..1..0....0..1..0....0..1..0

CROSSREFS

Columns 1..5 are A000110(n-1), A207864, A207865, A207866, A207867.

Main diagonal is A207863.

Cf. A207997 (3 colorings), A198715 (4 colorings), A198906 (5 colorings), A198982 (6 colorings), A198723 (7 colorings), A198914 (8 colorings).

Cf. A207981, A208001 (knight), A208021 (king), A208054, A208096, A208301.

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Feb 21 2012

STATUS

approved

A207997

T(n,k) = number of n X k 0..2 arrays with new values 0..2 introduced in row major order and no element equal to any horizontal or vertical neighbor (colorings ignoring permutations of colors).

+10
19

1, 1, 1, 2, 3, 2, 4, 9, 9, 4, 8, 27, 41, 27, 8, 16, 81, 187, 187, 81, 16, 32, 243, 853, 1302, 853, 243, 32, 64, 729, 3891, 9075, 9075, 3891, 729, 64, 128, 2187, 17749, 63267, 96831, 63267, 17749, 2187, 128, 256, 6561, 80963, 441090, 1034073, 1034073, 441090, 80963

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,4

COMMENTS

Number of colorings of the grid graph P_n X P_k using a maximum of 3 colors up to permutation of the colors. - Andrew Howroyd, Jun 26 2017

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..544

R. J. Mathar, Counting 2-way monotonic terrace forms over rectangular landscapes, vixra:1511.0225, eq. (33)-(35).

Eric Weisstein's World of Mathematics, Grid Graph

Eric Weisstein's World of Mathematics, Vertex Coloring

Wikipedia, Graph Coloring

FORMULA

2*T(n,m) = A078099(n,m) for m>1. - R. J. Mathar, Nov 23 2015

EXAMPLE

Table starts

..1....1.....2.......4.........8.........16...........32............64

..1....3.....9......27........81........243..........729..........2187

..2....9....41.....187.......853.......3891........17749.........80963

..4...27...187....1302......9075......63267.......441090.......3075255

..8...81...853....9075.....96831....1034073.....11045757.....117997043

.16..243..3891...63267...1034073...16932816....277458045....4547477370

.32..729.17749..441090..11045757..277458045...6978332618..175605187731

.64.2187.80963.3075255.117997043.4547477370.175605187731.6787438272198

...

Some solutions for n=4, k=3:

..0..1..2....0..1..0....0..1..0....0..1..2....0..1..2....0..1..2....0..1..0

..2..0..1....2..0..2....1..0..2....1..2..1....2..0..1....1..2..1....1..2..1

..0..2..0....0..1..0....2..1..0....0..1..2....0..2..0....0..1..2....2..0..2

..1..0..1....1..2..1....1..0..1....1..2..0....2..0..2....2..0..1....1..2..0

CROSSREFS

Cf. A020698 (column 3), A078100 (column 4), A207994 (column 5), A207995 (column 6), A207996 (column 7).

Main diagonal is A207993.

Cf. A198715 (4 colorings), A198906 (5 colorings), A198982 (6 colorings), A198723 (7 colorings), A198914 (8 colorings), A207868 (unlimited).

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Feb 22 2012

STATUS

approved

A198906

T(n,k) = number of n X k 0..4 arrays with values 0..4 introduced in row major order and no element equal to any horizontal or vertical neighbor.

+10
17

1, 1, 1, 2, 4, 2, 5, 33, 33, 5, 15, 380, 1211, 380, 15, 51, 4801, 50384, 50384, 4801, 51, 187, 62004, 2125425, 6907736, 2125425, 62004, 187, 715, 804833, 89793204, 948656912, 948656912, 89793204, 804833, 715, 2795, 10459180, 3794115705

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,4

COMMENTS

Number of colorings of the grid graph P_n X P_k using a maximum of 5 colors up to permutation of the colors. - Andrew Howroyd, Jun 26 2017

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..378 (terms 1..127 from R. H. Hardin)

EXAMPLE

Table starts

.....1..........1...............2....................5

.....1..........4..............33..................380

.....2.........33............1211................50384

.....5........380...........50384..............6907736

....15.......4801.........2125425............948656912

....51......62004........89793204.........130292546801

...187.....804833......3794115705.......17895005957823

...715...10459180....160319061892.....2457786852894234

..2795..135958401...6774239755817...337564362706067534

.11051.1767426404.286243775060868.46362726246946052884

...

Some solutions with values 0 to 4 for n=6, k=4:

..0..1..0..1....0..1..0..1....0..1..0..1....0..1..0..1....0..1..0..1

..1..0..1..0....1..0..1..0....1..0..1..0....1..0..1..0....1..0..1..0

..0..1..0..2....0..1..0..2....0..1..0..2....0..1..0..2....0..1..0..2

..2..0..2..0....2..0..3..0....2..0..2..3....2..0..1..0....2..0..1..3

..3..2..1..4....0..1..0..4....0..4..0..2....3..2..4..3....0..3..4..2

..2..4..2..1....2..4..3..1....1..3..1..4....1..0..1..2....4..0..1..4

CROSSREFS

Columns 1-7 are A007581(n-2), A198900, A198901, A198902, A198903, A198904, A198905.

Main diagonal is A198899.

Cf. A207997 (3 colorings), A198715 (4 colorings), A222144 (labeled 5 colorings), A198982 (6 colorings), A198723 (7 colorings), A198914 (8 colorings), A207868 (unlimited).

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Oct 31 2011

STATUS

approved

A198982

T(n,k) = number of n X k 0..5 arrays with values 0..5 introduced in row major order and no element equal to any horizontal or vertical neighbor.

+10
16

1, 1, 1, 2, 4, 2, 5, 34, 34, 5, 15, 481, 1835, 481, 15, 52, 8731, 146286, 146286, 8731, 52, 202, 174454, 12662226, 53082012, 12662226, 174454, 202, 855, 3603244, 1112962873, 19622872903, 19622872903, 1112962873, 3603244, 855, 3845, 75251971

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,4

COMMENTS

Number of colorings of the grid graph P_n X P_k using a maximum of 6 colors up to permutation of the colors. - Andrew Howroyd, Jun 26 2017

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..325 (terms 1..111 from R. H. Hardin)

EXAMPLE

Table starts

.....1...........1.................2........................5

.....1...........4................34......................481

.....2..........34..............1835...................146286

.....5.........481............146286.................53082012

....15........8731..........12662226..............19622872903

....52......174454........1112962873............7267830860056

...202.....3603244.......98102456246.........2692353648978984

...855....75251971.....8651794282083.......997397244990907738

..3845..1577395861...763087851014929....369492074075459555844

.18002.33105096904.67305520316532514.136880688981914387733120

...

Some solutions with all values from 0 to 5 for n=6, k=4:

..0..1..0..1....0..1..0..1....0..1..0..1....0..1..0..1....0..1..0..1

..1..2..3..0....1..2..3..0....1..2..3..0....1..2..3..0....1..2..3..0

..0..3..0..1....0..3..0..1....0..3..0..1....0..3..0..1....0..3..0..1

..2..0..3..0....1..0..3..0....1..0..3..0....1..0..3..0....1..0..3..0

..1..2..0..2....4..1..0..1....3..1..0..4....3..4..2..1....3..4..2..5

..4..5..2..1....5..4..2..4....5..2..3..1....1..5..1..5....5..1..5..2

CROSSREFS

Columns 1-7 are A056272(n-1), A198976, A198977, A198978, A198979, A198980, A198981.

Main diagonal is A198975.

Cf. A207997 (3 colorings), A198715 (4 colorings), A198906 (5 colorings), A222281 (labeled 6 colorings), A198723 (7 colorings), A198914 (8 colorings), A207868 (unlimited).

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Nov 01 2011

STATUS

approved

A198723

T(n,k) = number of n X k 0..6 arrays with values 0..6 introduced in row major order and no element equal to any horizontal or vertical neighbor.

+10
15

1, 1, 1, 2, 4, 2, 5, 34, 34, 5, 15, 499, 2027, 499, 15, 52, 10507, 232841, 232841, 10507, 52, 203, 272410, 34003792, 173549032, 34003792, 272410, 203, 876, 7817980, 5315840795, 141168480719, 141168480719, 5315840795, 7817980, 876, 4111

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,4

COMMENTS

Number of colorings of the grid graph P_n X P_k using a maximum of 7 colors up to permutation of the colors. - Andrew Howroyd, Jun 26 2017

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..325 (terms 1..84 from R. H. Hardin)

EXAMPLE

Table starts

.....1............1...................2.......................5

.....1............4..................34.....................499

.....2...........34................2027..................232841

.....5..........499..............232841...............173549032

....15........10507............34003792............141168480719

....52.......272410..........5315840795.........116492275674072

...203......7817980........846047363854.......96356630422085931

...876....234638905.....135284283124811....79732515488691835557

..4111...7176366133...21658679381667910.65980773070548173552412

.20648.221220625936.3468618095206638077

...

Some solutions with all values 0 to 6 for n=3, k=3:

..0..1..2....0..1..2....0..1..2....0..1..2....0..1..2....0..1..0....0..1..2

..3..2..4....2..3..1....3..4..5....1..3..4....3..4..3....2..3..4....3..4..3

..4..5..6....4..5..6....6..2..4....5..0..6....1..5..6....5..4..6....5..6..2

CROSSREFS

Columns 1-7 are A056273(n-1), A198717, A198718, A198719, A198720, A198721, A198722.

Main diagonal is A198716.

Cf. A207997 (3 colorings), A198715 (4 colorings), A198906 (5 colorings), A198982 (6 colorings), A222340 (labeled 7 colorings), A198914 (8 colorings), A207868 (unlimited).

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Oct 29 2011

STATUS

approved

A198914

T(n,k) = number of n X k 0..7 arrays with values 0..7 introduced in row major order and no element equal to any horizontal or vertical neighbor.

+10
15

1, 1, 1, 2, 4, 2, 5, 34, 34, 5, 15, 500, 2051, 500, 15, 52, 10867, 269940, 269940, 10867, 52, 203, 313132, 54381563, 319608038, 54381563, 313132, 203, 877, 10856948, 13088156547, 481871809749, 481871809749, 13088156547, 10856948, 877, 4139

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,4

COMMENTS

Number of colorings of the grid graph P_n X P_k using a maximum of 8 colors up to permutation of the colors. - Andrew Howroyd, Jun 26 2017

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..276 (terms 1..71 from R. H. Hardin)

EXAMPLE

Table starts

.....1............1..................2......................5

.....1............4.................34....................500

.....2...........34...............2051.................269940

.....5..........500.............269940..............319608038

....15........10867...........54381563...........481871809749

....52.......313132........13088156547........769126451071174

...203.....10856948......3352514013159....1243368053336112649

...877....418689772....876632051686733.2015791720035206825303

..4139..17067989413.230783525290600476

.21110.715189507700

...

Some solutions with values 0 to 7 for n=5, k=3:

..0..1..0....0..1..0....0..1..0....0..1..0....0..1..0....0..1..0....0..1..0

..1..2..1....1..0..1....1..2..1....1..0..2....1..0..2....1..2..3....1..2..3

..3..0..2....2..3..4....3..4..2....3..4..5....3..4..5....0..1..4....0..4..5

..2..4..5....5..4..3....5..6..1....5..3..6....6..7..0....5..6..7....1..5..1

..1..6..7....6..0..7....6..7..2....7..4..2....3..0..3....7..0..5....6..7..4

CROSSREFS

Columns 1-7 are A099262(n-1), A198908, A198909, A198910, A198911, A198912, A198913.

Main diagonal is A198907.

Cf. A207997 (3 colorings), A198715 (4 colorings), A198906 (5 colorings), A198982 (6 colorings), A198723 (7 colorings), A222462 (labeled 8 colorings), A207868 (unlimited).

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Oct 31 2011

STATUS

approved

A222444

T(n,k) = number of n X k 0..3 arrays with entries increasing mod 4 by 0, 1 or 2 rightwards and downwards, starting with upper left zero.

+10
14

1, 3, 3, 9, 21, 9, 27, 147, 147, 27, 81, 1029, 2403, 1029, 81, 243, 7203, 39285, 39285, 7203, 243, 729, 50421, 642249, 1500183, 642249, 50421, 729, 2187, 352947, 10499787, 57289767, 57289767, 10499787, 352947, 2187, 6561, 2470629, 171655443

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

1/4 the number of 4-colorings of the grid graph P_n X P_k. - Andrew Howroyd, Jun 26 2017

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..496 (terms 1..180 from R. H. Hardin)

Eric Weisstein's World of Mathematics, Grid Graph

Eric Weisstein's World of Mathematics, Vertex Coloring

Wikipedia, Graph Coloring

FORMULA

T(n,k) = 6*A198715(n,k) - 3 for n*k>1. - Andrew Howroyd, Jun 27 2017

Empirical for column k:

k=1: a(n) = 3*a(n-1).

k=2: a(n) = 7*a(n-1).

k=3: a(n) = 18*a(n-1) - 27*a(n-2).

k=4: a(n) = 45*a(n-1) - 267*a(n-2) + 263*a(n-3).

k=5: a(n) = 118*a(n-1) - 2811*a(n-2) + 22255*a(n-3) - 53860*a(n-4) - 54747*a(n-5) + 269406*a(n-6) - 175392*a(n-7).

k=6: [order 13]

k=7: [order 32]

EXAMPLE

Table starts

......1..........3...............9..................27.......................81

......3.........21.............147................1029.....................7203

......9........147............2403...............39285...................642249

.....27.......1029...........39285.............1500183.................57289767

.....81.......7203..........642249............57289767...............5110723191

....243......50421........10499787..........2187822609.............455924913093

....729.....352947.......171655443.........83550197745...........40672916404629

...2187....2470629......2806303725.......3190677470643.........3628419487925547

...6561...17294403.....45878770089.....121847980727187.......323690312271131451

..19683..121060821....750047661027....4653221950068669.....28876324830999722133

..59049..847425747..12262131106083..177700725073710285...2576049100980154511889

.177147.5931980229.200467073061765.6786168386579878383.229808641254065144560647

...

Some solutions for n=3, k=4:

..0..0..0..2....0..0..2..0....0..2..0..0....0..2..0..2....0..0..2..3

..1..2..2..3....0..2..3..1....2..2..2..0....0..0..0..2....0..2..3..1

..2..2..3..1....2..0..1..3....2..2..0..0....2..0..1..3....1..2..0..1

CROSSREFS

Columns 1-7 are A000244(n-1), A169634(n-1), A222439, A222440, A222441, A222442, A222443.

Main diagonal is A068254.

Cf. A078099 (3 colorings), A198715 (unlabeled 4 colorings), A222144 (5 colorings), A222281 (6 colorings), A222340 (7 colorings), A222462 (8 colorings).

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Feb 20 2013

STATUS

approved

A222281

T(n,k) = number of n X k 0..5 arrays with no entry increasing mod 6 by 5 rightwards or downwards, starting with upper left zero.

+10
13

1, 5, 5, 25, 105, 25, 125, 2205, 2205, 125, 625, 46305, 194485, 46305, 625, 3125, 972405, 17153945, 17153945, 972405, 3125, 15625, 20420505, 1513010465, 6354787485, 1513010465, 20420505, 15625, 78125, 428830605, 133450391205

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

1/6 the number of 6-colorings of the grid graph P_n X P_k. - Andrew Howroyd, Jun 26 2017

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..325 (terms 1..111 from R. H. Hardin)

FORMULA

T(n, k) = 5 * (24*A198982(n,k) - 12*A198715(n,k) - 8*A207997(n,k) - 3) for n*k > 1. - Andrew Howroyd, Jun 27 2017

EXAMPLE

Table starts

........1................5......................25..........................125

........5..............105....................2205........................46305

.......25.............2205..................194485.....................17153945

......125............46305................17153945...................6354787485

......625...........972405..............1513010465................2354171487645

.....3125.........20420505............133450391205..............872117822449905

....15625........428830605..........11770577485085...........323081602357856985

....78125.......9005442705........1038187247574145........119687637492011211885

...390625.....189114296805.......91570083319317865......44339047670574481807485

..1953125....3971400232905.....8076654937439905005...16425682631297501047982145

..9765625...83399404891005...712376276332499775685.6084998755694142903356375385

.48828125.1751387502711105.62832938018547611186345

...

Some solutions for n=3, k=4:

..0..0..0..0....0..0..0..0....0..0..0..0....0..3..0..0....0..0..0..0

..4..2..0..1....1..2..0..4....0..0..0..1....0..0..3..1....0..2..3..0

..0..4..1..4....1..4..1..2....3..4..4..1....3..0..4..4....4..5..1..3

CROSSREFS

Columns 1-7 are A000351(n-1), 5*A009965(n-1), A222276, A222277, A222278, A222279, A222280.

Main diagonal is A068256.

Cf. A078099 (3 colorings), A222444 (4 colorings), A222144 (5 colorings), A198982 (unlabeled 6 colorings), A222340 (7 colorings), A222462 (8 colorings).

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Feb 14 2013

STATUS

approved

A222340

T(n,k) = number of n X k 0..6 arrays with no entry increasing mod 7 by 6 rightwards or downwards, starting with upper left zero.

+10
13

1, 6, 6, 36, 186, 36, 216, 5766, 5766, 216, 1296, 178746, 923526, 178746, 1296, 7776, 5541126, 147918906, 147918906, 5541126, 7776, 46656, 171774906, 23691810366, 122408393436, 23691810366, 171774906, 46656, 279936, 5325022086

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

1/7 the number of 7-colorings of the grid graph P_n X P_k. - Andrew Howroyd, Jun 26 2017

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..325 (terms 1..84 from R. H. Hardin)

FORMULA

T(n, k) = 6 * (120*A198723(n,k) - 60*A198906(n,k) - 40*A198715(n,k) - 15*A207997(n,k) - 4) for n*k > 1. - Andrew Howroyd, Jun 27 2017

EXAMPLE

Table starts

.......1.............6...................36........................216

.......6...........186.................5766.....................178746

......36..........5766...............923526..................147918906

.....216........178746............147918906...............122408393436

....1296.......5541126..........23691810366............101297497221786

....7776.....171774906........3794659477146..........83827445649884946

...46656....5325022086......607781352505806.......69370328359709445996

..279936..165075684666....97346856728146986....57406526220963704077986

.1679616.5117346224646.15591808593304758846.47506035082750189614687546

...

Some solutions for n=3, k=4:

..0..0..2..0....0..2..2..0....0..0..0..0....0..2..0..0....0..2..0..0

..0..5..3..0....0..2..5..0....0..1..5..0....0..5..0..0....0..0..5..0

..3..1..4..5....4..4..2..3....3..6..1..4....2..2..2..2....4..1..3..4

CROSSREFS

Columns 1-6 are A000400(n-1), A222335, A222336, A222337, A222338, A222339.

Main diagonal is A068257.

Cf. A078099 (3 colorings), A222444 (4 colorings), A222144 (5 colorings), A222281 (6 colorings), A198723 (unlabeled 7 colorings), A222462 (8 colorings).

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Feb 15 2013

STATUS

approved

A222462

T(n,k) = number of n X k 0..7 arrays with no entry increasing mod 8 by 7 rightwards or downwards, starting with upper left zero.

+10
11

1, 7, 7, 49, 301, 49, 343, 12943, 12943, 343, 2401, 556549, 3418807, 556549, 2401, 16807, 23931607, 903055069, 903055069, 23931607, 16807, 117649, 1029059101, 238535974201, 1465295106499, 238535974201, 1029059101, 117649, 823543

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

1/8 the number of 8-colorings of the grid graph P_n X P_k. - Andrew Howroyd, Jun 26 2017

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..276 (terms 1..83 from R. H. Hardin)

FORMULA

T(n, k) = 7 * (720*A198914(n,k) - 360*A198982(n,k) - 240*A198906(n,k) - 90*A198715(n,k) - 24*A207997(n,k) - 5) for n*k > 1. - Andrew Howroyd, Jun 27 2017

Empirical for column k:

k=1: a(n) = 7*a(n-1).

k=2: a(n) = 43*a(n-1).

k=3: a(n) = 270*a(n-1) - 1547*a(n-2).

k=4: a(n) = 1689*a(n-1) - 108775*a(n-2) + 1672631*a(n-3).

k=5: a(n) = 10754*a(n-1) - 8060499*a(n-2) + 2219242223*a(n-3) - 245682627864*a(n-4) + 5798947687589*a(n-5) + 448113231493438*a(n-6) - 2763020698450992*a(n-7).

EXAMPLE

Table starts

......1.............7..................49........................343

......7...........301...............12943.....................556549

.....49.........12943.............3418807..................903055069

....343........556549...........903055069..............1465295106499

...2401......23931607........238535974201...........2377584520856755

..16807....1029059101......63007686842527........3857863258420747009

.117649...44249541343...16643060295393343.....6259760185235726701945

.823543.1902730277749.4396153388210813341.10157072698503130798653535

...

Some solutions for n=3, k=4:

..0..4..2..3....0..0..0..4....0..4..6..1....0..4..0..4....0..2..6..2

..0..0..5..6....0..0..4..6....0..0..1..5....0..0..6..0....0..0..2..3

..0..0..0..1....0..0..5..1....0..0..3..5....0..0..0..1....0..0..3..5

CROSSREFS

Columns 1-5 are A000420(n-1), 7*43^(n-1), A222459, A222460, A222461.

Main diagonal is A068258.

Cf. A078099 (3 colorings), A222444 (4 colorings), A222144 (5 colorings), A222281 (6 colorings), A222340 (7 colorings), A198914 (unlabeled 8 colorings).

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Feb 21 2013

STATUS

approved