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 A222281 T(n,k) = number of n X k 0..5 arrays with no entry increasing mod 6 by 5 rightwards or downwards, starting with upper left zero. 13
 1, 5, 5, 25, 105, 25, 125, 2205, 2205, 125, 625, 46305, 194485, 46305, 625, 3125, 972405, 17153945, 17153945, 972405, 3125, 15625, 20420505, 1513010465, 6354787485, 1513010465, 20420505, 15625, 78125, 428830605, 133450391205 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 1/6 the number of 6-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..111 from R. H. Hardin) FORMULA T(n, k) = 5 * (24*A198982(n,k) - 12*A198715(n,k) - 8*A207997(n,k) - 3) for n*k > 1. - Andrew Howroyd, Jun 27 2017 EXAMPLE Table starts ........1................5......................25..........................125 ........5..............105....................2205........................46305 .......25.............2205..................194485.....................17153945 ......125............46305................17153945...................6354787485 ......625...........972405..............1513010465................2354171487645 .....3125.........20420505............133450391205..............872117822449905 ....15625........428830605..........11770577485085...........323081602357856985 ....78125.......9005442705........1038187247574145........119687637492011211885 ...390625.....189114296805.......91570083319317865......44339047670574481807485 ..1953125....3971400232905.....8076654937439905005...16425682631297501047982145 ..9765625...83399404891005...712376276332499775685.6084998755694142903356375385 .48828125.1751387502711105.62832938018547611186345 ... Some solutions for n=3, k=4: ..0..0..0..0....0..0..0..0....0..0..0..0....0..3..0..0....0..0..0..0 ..4..2..0..1....1..2..0..4....0..0..0..1....0..0..3..1....0..2..3..0 ..0..4..1..4....1..4..1..2....3..4..4..1....3..0..4..4....4..5..1..3 CROSSREFS Columns 1-7 are A000351(n-1), 5*A009965(n-1), A222276, A222277, A222278, A222279, A222280. Main diagonal is A068256. Cf. A078099 (3 colorings), A222444 (4 colorings), A222144 (5 colorings), A198982 (unlabeled 6 colorings), A222340 (7 colorings), A222462 (8 colorings). Sequence in context: A257615 A257624 A176160 * A214706 A203191 A165423 Adjacent sequences:  A222278 A222279 A222280 * A222282 A222283 A222284 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Feb 14 2013 STATUS approved

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Last modified January 21 17:55 EST 2022. Contains 350479 sequences. (Running on oeis4.)