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.

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

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).

Sequence in context: A242087 A217978 A257626 * A215270 A203057 A165424

Adjacent sequences: A222337 A222338 A222339 * A222341 A222342 A222343

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 15 2013

Status

approved