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A302680 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

%I A302680 #4 Apr 11 2018 12:28:33
%S A302680 1,2,2,3,3,4,5,3,4,8,8,5,8,6,16,13,7,12,7,9,32,21,13,18,20,11,14,64,
%T A302680 34,23,40,30,33,18,22,128,55,37,94,76,63,64,29,35,256,89,63,184,217,
%U A302680 187,125,121,47,56,512,144,109,358,509,661,453,257,231,76,90,1024,233,183,760
%N A302680 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
%C A302680 Table starts
%C A302680 ...1..2..3...5....8...13....21.....34......55.......89......144.......233
%C A302680 ...2..3..3...5....7...13....23.....37......63......109......183.......309
%C A302680 ...4..4..8..12...18...40....94....184.....358......760.....1594......3220
%C A302680 ...8..6..7..20...30...76...217....509....1189.....3034.....7569.....18274
%C A302680 ..16..9.11..33...63..187...661...1837....5075....15661....46975....135191
%C A302680 ..32.14.18..64..125..453..2013...6725...21745....80985...295335...1015113
%C A302680 ..64.22.29.121..257.1125..6311..25139...96728...439233..1942666...8017639
%C A302680 .128.35.47.231..528.2782.19497..92889..422915..2330640.12480973..61679118
%C A302680 .256.56.76.440.1085.6843.60253.343421.1847358.12346637.80210343.474618407
%H A302680 R. H. Hardin, <a href="/A302680/b302680.txt">Table of n, a(n) for n = 1..799</a>
%F A302680 Empirical for column k:
%F A302680 k=1: a(n) = 2*a(n-1)
%F A302680 k=2: a(n) = 2*a(n-1) -a(n-3)
%F A302680 k=3: a(n) = a(n-1) +a(n-2) for n>5
%F A302680 k=4: a(n) = a(n-1) +2*a(n-2) -a(n-4) for n>8
%F A302680 k=5: a(n) = a(n-1) +3*a(n-3) +2*a(n-4) +2*a(n-5) for n>10
%F A302680 k=6: a(n) = a(n-1) +2*a(n-2) +4*a(n-3) +a(n-4) -2*a(n-5) -a(n-6) for n>12
%F A302680 k=7: [order 12] for n>19
%F A302680 Empirical for row n:
%F A302680 n=1: a(n) = a(n-1) +a(n-2)
%F A302680 n=2: a(n) = a(n-1) +2*a(n-3) for n>5
%F A302680 n=3: a(n) = a(n-1) +3*a(n-3) +3*a(n-4) for n>7
%F A302680 n=4: a(n) = a(n-1) +a(n-2) +5*a(n-3) +5*a(n-4) -3*a(n-5) -3*a(n-6) +2*a(n-7) for n>11
%F A302680 n=5: [order 11] for n>16
%F A302680 n=6: [order 17] for n>23
%F A302680 n=7: [order 31] for n>38
%e A302680 Some solutions for n=5 k=4
%e A302680 ..0..1..1..1. .0..1..0..1. .0..0..0..1. .0..1..1..1. .0..0..0..1
%e A302680 ..0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1. .0..1..0..1
%e A302680 ..0..1..0..1. .0..0..1..1. .0..1..1..1. .0..1..0..1. .0..1..0..1
%e A302680 ..0..1..0..1. .1..1..0..0. .0..1..0..1. .0..1..0..1. .0..1..0..1
%e A302680 ..0..0..0..1. .1..0..1..0. .0..1..0..1. .0..1..0..1. .0..1..0..1
%Y A302680 Column 1 is A000079(n-1).
%Y A302680 Column 2 is A001611(n+1).
%Y A302680 Row 1 is A000045(n+1).
%Y A302680 Row 2 is A003229(n-1) for n>2.
%K A302680 nonn,tabl
%O A302680 1,2
%A A302680 _R. H. Hardin_, Apr 11 2018