%I #12 Jun 28 2017 02:10:54

%S 1,6,6,36,186,36,216,5766,5766,216,1296,178746,923526,178746,1296,

%T 7776,5541126,147918906,147918906,5541126,7776,46656,171774906,

%U 23691810366,122408393436,23691810366,171774906,46656,279936,5325022086

%N 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.

%C 1/7 the number of 7-colorings of the grid graph P_n X P_k. - _Andrew Howroyd_, Jun 26 2017

%H Andrew Howroyd, <a href="/A222340/b222340.txt">Table of n, a(n) for n = 1..325</a> (terms 1..84 from R. H. Hardin)

%F 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

%e Table starts

%e .......1.............6...................36........................216

%e .......6...........186.................5766.....................178746

%e ......36..........5766...............923526..................147918906

%e .....216........178746............147918906...............122408393436

%e ....1296.......5541126..........23691810366............101297497221786

%e ....7776.....171774906........3794659477146..........83827445649884946

%e ...46656....5325022086......607781352505806.......69370328359709445996

%e ..279936..165075684666....97346856728146986....57406526220963704077986

%e .1679616.5117346224646.15591808593304758846.47506035082750189614687546

%e ...

%e Some solutions for n=3, k=4:

%e ..0..0..2..0....0..2..2..0....0..0..0..0....0..2..0..0....0..2..0..0

%e ..0..5..3..0....0..2..5..0....0..1..5..0....0..5..0..0....0..0..5..0

%e ..3..1..4..5....4..4..2..3....3..6..1..4....2..2..2..2....4..1..3..4

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

%Y Main diagonal is A068257.

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

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Feb 15 2013