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A302808 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

%I A302808 #4 Apr 13 2018 13:09:15
%S A302808 1,2,2,4,8,4,8,29,32,8,16,105,169,128,16,32,384,934,1010,512,32,64,
%T A302808 1405,5117,8718,6084,2048,64,128,5135,28128,74072,82367,36456,8192,
%U A302808 128,256,18766,154494,632004,1089773,773520,218640,32768,256,512,68589,848519
%N A302808 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
%C A302808 Table starts
%C A302808 ...1......2.......4.........8..........16............32..............64
%C A302808 ...2......8......29.......105.........384..........1405............5135
%C A302808 ...4.....32.....169.......934........5117.........28128..........154494
%C A302808 ...8....128....1010......8718.......74072........632004.........5396562
%C A302808 ..16....512....6084.....82367.....1089773......14458177.......192211013
%C A302808 ..32...2048...36456....773520....15904814.....327603711......6769884156
%C A302808 ..64...8192..218640...7267160...232260380....7428713676....238687785290
%C A302808 .128..32768.1312416..68346451..3396923500..168777255305...8434497360938
%C A302808 .256.131072.7873344.642498696.49653502029.3832039683236.297820640670676
%H A302808 R. H. Hardin, <a href="/A302808/b302808.txt">Table of n, a(n) for n = 1..180</a>
%F A302808 Empirical for column k:
%F A302808 k=1: a(n) = 2*a(n-1)
%F A302808 k=2: a(n) = 4*a(n-1)
%F A302808 k=3: a(n) = 6*a(n-1) +24*a(n-3) -144*a(n-4) for n>6
%F A302808 k=4: [order 18] for n>20
%F A302808 k=5: [order 90] for n>92
%F A302808 Empirical for row n:
%F A302808 n=1: a(n) = 2*a(n-1)
%F A302808 n=2: a(n) = 3*a(n-1) +a(n-2) +4*a(n-3) +4*a(n-4)
%F A302808 n=3: [order 13] for n>15
%F A302808 n=4: [order 48] for n>50
%e A302808 Some solutions for n=5 k=4
%e A302808 ..0..1..0..0. .0..0..0..0. .0..0..1..0. .0..0..1..0. .0..1..1..0
%e A302808 ..1..0..1..1. .0..1..1..0. .1..0..1..0. .0..0..1..1. .1..1..1..1
%e A302808 ..1..0..1..0. .0..1..0..1. .1..0..1..1. .0..0..1..1. .0..0..0..0
%e A302808 ..0..1..0..1. .0..0..0..0. .1..0..0..0. .1..0..1..1. .0..1..1..0
%e A302808 ..1..1..0..0. .0..0..1..1. .1..0..1..0. .1..0..1..0. .1..1..1..1
%Y A302808 Column 1 is A000079(n-1).
%Y A302808 Column 2 is A004171(n-1).
%Y A302808 Row 1 is A000079(n-1).
%Y A302808 Row 2 is A302266.
%K A302808 nonn,tabl
%O A302808 1,2
%A A302808 _R. H. Hardin_, Apr 13 2018