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 A208054 T(n,k) = Number of n X k nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to any horizontal, vertical or antidiagonal neighbor (colorings ignoring permutations of colors). 6
 1, 1, 1, 2, 2, 2, 5, 15, 15, 5, 15, 203, 716, 203, 15, 52, 4140, 83440, 83440, 4140, 52, 203, 115975, 18171918, 112073062, 18171918, 115975, 203, 877, 4213597, 6423127757, 346212384169, 346212384169, 6423127757, 4213597, 877, 4140, 190899322 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Equivalently, the number of colorings in the rhombic hexagonal square grid graph RH_(n,k) using any number of colors up to permutation of the colors. - Andrew Howroyd, Jun 25 2017 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..231 (terms 1..49 from R. H. Hardin) EXAMPLE Table starts ...1.........1.............2................5................15 ...1.........2............15..............203..............4140 ...2........15...........716............83440..........18171918 ...5.......203.........83440........112073062......346212384169 ..15......4140......18171918.....346212384169.18633407199331522 ..52....115975....6423127757.2043836452962923 .203...4213597.3376465219485 .877.190899322 ... Some solutions for n=4 k=3 ..0..1..0....0..1..0....0..1..0....0..1..0....0..1..2....0..1..0....0..1..0 ..2..3..1....2..3..4....2..3..2....2..3..1....2..3..0....2..3..1....2..3..2 ..4..2..4....0..5..0....0..4..0....0..4..5....4..5..3....4..5..3....0..1..4 ..0..5..0....1..2..1....1..2..1....5..3..4....0..1..0....0..6..4....2..0..1 CROSSREFS Columns 1-5 are A000110(n-1), A020557(n-1), A208051, A208052, A208053. Cf. A207868, A212162, A212163, A208050, A068271. Sequence in context: A116697 A014244 A216634 * A059814 A079443 A270380 Adjacent sequences:  A208051 A208052 A208053 * A208055 A208056 A208057 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Feb 22 2012 STATUS approved

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Last modified May 27 21:52 EDT 2020. Contains 334671 sequences. (Running on oeis4.)