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 A222444 T(n,k) = number of n X k 0..3 arrays with entries increasing mod 4 by 0, 1 or 2 rightwards and downwards, starting with upper left zero. 14
 1, 3, 3, 9, 21, 9, 27, 147, 147, 27, 81, 1029, 2403, 1029, 81, 243, 7203, 39285, 39285, 7203, 243, 729, 50421, 642249, 1500183, 642249, 50421, 729, 2187, 352947, 10499787, 57289767, 57289767, 10499787, 352947, 2187, 6561, 2470629, 171655443 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 1/4 the number of 4-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..496 (terms 1..180 from R. H. Hardin) Eric Weisstein's World of Mathematics, Grid Graph Eric Weisstein's World of Mathematics, Vertex Coloring Wikipedia, Graph Coloring FORMULA T(n,k) = 6*A198715(n,k) - 3 for n*k>1. - Andrew Howroyd, Jun 27 2017 Empirical for column k: k=1: a(n) = 3*a(n-1). k=2: a(n) = 7*a(n-1). k=3: a(n) = 18*a(n-1) - 27*a(n-2). k=4: a(n) = 45*a(n-1) - 267*a(n-2) + 263*a(n-3). k=5: a(n) = 118*a(n-1) - 2811*a(n-2) + 22255*a(n-3) - 53860*a(n-4) - 54747*a(n-5) + 269406*a(n-6) - 175392*a(n-7). k=6: [order 13] k=7: [order 32] EXAMPLE Table starts ......1..........3...............9..................27.......................81 ......3.........21.............147................1029.....................7203 ......9........147............2403...............39285...................642249 .....27.......1029...........39285.............1500183.................57289767 .....81.......7203..........642249............57289767...............5110723191 ....243......50421........10499787..........2187822609.............455924913093 ....729.....352947.......171655443.........83550197745...........40672916404629 ...2187....2470629......2806303725.......3190677470643.........3628419487925547 ...6561...17294403.....45878770089.....121847980727187.......323690312271131451 ..19683..121060821....750047661027....4653221950068669.....28876324830999722133 ..59049..847425747..12262131106083..177700725073710285...2576049100980154511889 .177147.5931980229.200467073061765.6786168386579878383.229808641254065144560647 ... Some solutions for n=3, k=4: ..0..0..0..2....0..0..2..0....0..2..0..0....0..2..0..2....0..0..2..3 ..1..2..2..3....0..2..3..1....2..2..2..0....0..0..0..2....0..2..3..1 ..2..2..3..1....2..0..1..3....2..2..0..0....2..0..1..3....1..2..0..1 CROSSREFS Columns 1-7 are A000244(n-1), A169634(n-1), A222439, A222440, A222441, A222442, A222443. Main diagonal is A068254. Cf. A078099 (3 colorings), A198715 (unlabeled 4 colorings), A222144 (5 colorings), A222281 (6 colorings), A222340 (7 colorings), A222462 (8 colorings). Sequence in context: A099465 A099094 A222169 * A206492 A007683 A316220 Adjacent sequences:  A222441 A222442 A222443 * A222445 A222446 A222447 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Feb 20 2013 STATUS approved

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Last modified January 22 16:29 EST 2020. Contains 331152 sequences. (Running on oeis4.)