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 A268886 T(n,k)=Number of nXk binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once. 13
 0, 1, 0, 2, 5, 0, 5, 14, 20, 0, 10, 54, 84, 71, 0, 20, 158, 501, 462, 235, 0, 38, 475, 2190, 4133, 2418, 744, 0, 71, 1340, 9996, 27130, 31956, 12252, 2285, 0, 130, 3740, 42362, 186732, 317966, 236960, 60666, 6865, 0, 235, 10204, 178400, 1187838, 3283890 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Table starts .0.....1.......2.........5..........10............20..............38 .0.....5......14........54.........158...........475............1340 .0....20......84.......501........2190..........9996...........42362 .0....71.....462......4133.......27130........186732.........1187838 .0...235....2418.....31956......317966.......3283890........31427480 .0...744...12252....236960.....3596174......55491832.......800733668 .0..2285...60666...1706732....39670270.....911930096.....19876401224 .0..6865..295230..12034000...429588382...14681855846....483987898760 .0.20284.1417452..83485488..4585939726..232688402028..11611969197776 .0.59155.6732102.571836176.48401059362.3642322709900.275345016177616 LINKS R. H. Hardin, Table of n, a(n) for n = 1..799 FORMULA Empirical for column k: k=1: a(n) = a(n-1) k=2: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) -a(n-4) k=3: a(n) = 10*a(n-1) -31*a(n-2) +30*a(n-3) -9*a(n-4) k=4: a(n) = 16*a(n-1) -88*a(n-2) +200*a(n-3) -208*a(n-4) +96*a(n-5) -16*a(n-6) for n>7 k=5: [order 8] for n>9 k=6: [order 10] for n>12 k=7: [order 14] for n>16 Empirical for row n: n=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4) n=2: a(n) = 2*a(n-1) +5*a(n-2) -4*a(n-3) -11*a(n-4) -6*a(n-5) -a(n-6) n=3: [order 9] n=4: [order 16] n=5: [order 26] n=6: [order 42] n=7: [order 68] EXAMPLE Some solutions for n=4 k=4 ..0..1..0..0. .0..0..0..0. .0..0..1..0. .0..0..0..0. .0..1..0..0 ..0..0..0..1. .0..1..0..1. .1..0..0..1. .0..0..1..1. .0..1..0..0 ..0..0..1..0. .1..0..0..0. .1..0..0..0. .0..0..0..0. .0..1..0..0 ..1..0..1..0. .1..0..0..1. .1..1..0..1. .0..1..0..0. .1..0..0..0 CROSSREFS Column 2 is A054444(n-1). Row 1 is A001629. Sequence in context: A196816 A058204 A242969 * A090625 A021403 A299623 Adjacent sequences:  A268883 A268884 A268885 * A268887 A268888 A268889 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Feb 15 2016 STATUS approved

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Last modified July 25 23:39 EDT 2021. Contains 346294 sequences. (Running on oeis4.)