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

Offset: 1

Author

R. H. Hardin, Feb 09 2013

Keywords

• nonn
• tabl

Comments

1/5 the number of 5-colorings of the grid graph P_n X P_k. - Andrew Howroyd, Jun 26 2017

Examples

			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
		

Links

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

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).

Formula

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