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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.

%I A268886 #4 Feb 15 2016 11:33:56
%S A268886 0,1,0,2,5,0,5,14,20,0,10,54,84,71,0,20,158,501,462,235,0,38,475,2190,
%T A268886 4133,2418,744,0,71,1340,9996,27130,31956,12252,2285,0,130,3740,42362,
%U A268886 186732,317966,236960,60666,6865,0,235,10204,178400,1187838,3283890
%N A268886 T(n,k)=Number of nXk binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.
%C A268886 Table starts
%C A268886 .0.....1.......2.........5..........10............20..............38
%C A268886 .0.....5......14........54.........158...........475............1340
%C A268886 .0....20......84.......501........2190..........9996...........42362
%C A268886 .0....71.....462......4133.......27130........186732.........1187838
%C A268886 .0...235....2418.....31956......317966.......3283890........31427480
%C A268886 .0...744...12252....236960.....3596174......55491832.......800733668
%C A268886 .0..2285...60666...1706732....39670270.....911930096.....19876401224
%C A268886 .0..6865..295230..12034000...429588382...14681855846....483987898760
%C A268886 .0.20284.1417452..83485488..4585939726..232688402028..11611969197776
%C A268886 .0.59155.6732102.571836176.48401059362.3642322709900.275345016177616
%H A268886 R. H. Hardin, <a href="/A268886/b268886.txt">Table of n, a(n) for n = 1..799</a>
%F A268886 Empirical for column k:
%F A268886 k=1: a(n) = a(n-1)
%F A268886 k=2: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) -a(n-4)
%F A268886 k=3: a(n) = 10*a(n-1) -31*a(n-2) +30*a(n-3) -9*a(n-4)
%F A268886 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
%F A268886 k=5: [order 8] for n>9
%F A268886 k=6: [order 10] for n>12
%F A268886 k=7: [order 14] for n>16
%F A268886 Empirical for row n:
%F A268886 n=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4)
%F A268886 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)
%F A268886 n=3: [order 9]
%F A268886 n=4: [order 16]
%F A268886 n=5: [order 26]
%F A268886 n=6: [order 42]
%F A268886 n=7: [order 68]
%e A268886 Some solutions for n=4 k=4
%e A268886 ..0..1..0..0. .0..0..0..0. .0..0..1..0. .0..0..0..0. .0..1..0..0
%e A268886 ..0..0..0..1. .0..1..0..1. .1..0..0..1. .0..0..1..1. .0..1..0..0
%e A268886 ..0..0..1..0. .1..0..0..0. .1..0..0..0. .0..0..0..0. .0..1..0..0
%e A268886 ..1..0..1..0. .1..0..0..1. .1..1..0..1. .0..1..0..0. .1..0..0..0
%Y A268886 Column 2 is A054444(n-1).
%Y A268886 Row 1 is A001629.
%K A268886 nonn,tabl
%O A268886 1,4
%A A268886 _R. H. Hardin_, Feb 15 2016