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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. 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). 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

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Last modified June 3 23:57 EDT 2020. Contains 334808 sequences. (Running on oeis4.)