A222339 -id:A222339

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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

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