A222144 - OEIS

A222144

T(n,k) = number of n X k 0..4 arrays with no entry increasing mod 5 by 4 rightwards or downwards, starting with upper left zero.

1, 4, 4, 16, 52, 16, 64, 676, 676, 64, 256, 8788, 28564, 8788, 256, 1024, 114244, 1206964, 1206964, 114244, 1024, 4096, 1485172, 50999956, 165770032, 50999956, 1485172, 4096, 16384, 19307236, 2154990196, 22767656980, 22767656980

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OFFSET

1,2

COMMENTS

1/5 the number of 5-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..378 (terms 1..127 from R. H. Hardin)

FORMULA

T(n,k) = 4 * (6*A198906(n,k) - 3*A207997(n,k) - 2) for n*k > 1. - Andrew Howroyd, Jun 27 2017

EXAMPLE

Table starts

.......1.............4...................16.........................64

.......4............52..................676.......................8788

......16...........676................28564....................1206964

......64..........8788..............1206964..................165770032

.....256........114244.............50999956................22767656980

....1024.......1485172...........2154990196..............3127020364012

....4096......19307236..........91058563924............429480137694664

...16384.....250994068........3847656513844..........58986884432558548

...65536....3262922884......162581749707796........8101544704688334244

..262144...42417997492.....6869850581244916.....1112705429924911477552

.1048576..551433967396...290283793189916884...152824358676750267429220

.4194304.7168641576148.12265868026121849524.20989638386627725143014812

...

Some solutions for n=3, k=4:

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

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

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

CROSSREFS

Columns 1-7 are A000302(n-1), A222138, A222139, A222140, A222141, A222142, A222143.

Main diagonal is A068255.

Cf. A078099 (3 colorings), A222444 (4 colorings), A198906 (unlabeled 5 colorings), A222281 (6 colorings), A222340 (7 colorings), A222462 (8 colorings).

Sequence in context: A257613 A223202 A298448 * A342817 A107382 A257622

Adjacent sequences: A222141 A222142 A222143 * A222145 A222146 A222147

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Feb 09 2013

STATUS

approved