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A301841 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1 or 2 horizontally or antidiagonally adjacent elements, with upper left element zero.

%I A301841 #4 Mar 27 2018 14:31:28
%S A301841 1,2,2,4,8,4,8,25,32,8,16,81,139,128,16,32,263,678,773,512,32,64,855,
%T A301841 3182,5748,4299,2048,64,128,2778,15199,39703,48802,23909,8192,128,256,
%U A301841 9027,72514,281758,496085,414385,132971,32768,256,512,29333,346244
%N A301841 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1 or 2 horizontally or antidiagonally adjacent elements, with upper left element zero.
%C A301841 Table starts
%C A301841 ...1......2.......4.........8..........16...........32.............64
%C A301841 ...2......8......25........81.........263..........855...........2778
%C A301841 ...4.....32.....139.......678........3182........15199..........72514
%C A301841 ...8....128.....773......5748.......39703.......281758........1986213
%C A301841 ..16....512....4299.....48802......496085......5240684.......54948498
%C A301841 ..32...2048...23909....414385.....6196305.....97439921.....1518341751
%C A301841 ..64...8192..132971...3518619....77396422...1812097252....41966406867
%C A301841 .128..32768..739525..29877293...966770632..33701001773..1159968653556
%C A301841 .256.131072.4112907.253694309.12076215811.626769301255.32062561937804
%H A301841 R. H. Hardin, <a href="/A301841/b301841.txt">Table of n, a(n) for n = 1..417</a>
%F A301841 Empirical for column k:
%F A301841 k=1: a(n) = 2*a(n-1)
%F A301841 k=2: a(n) = 4*a(n-1)
%F A301841 k=3: a(n) = 7*a(n-1) -8*a(n-2) for n>3
%F A301841 k=4: a(n) = 13*a(n-1) -46*a(n-2) +72*a(n-3) -57*a(n-4) +16*a(n-5) for n>6
%F A301841 k=5: [order 11] for n>13
%F A301841 k=6: [order 25] for n>27
%F A301841 k=7: [order 53] for n>56
%F A301841 Empirical for row n:
%F A301841 n=1: a(n) = 2*a(n-1)
%F A301841 n=2: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4) for n>6
%F A301841 n=3: [order 12] for n>14
%F A301841 n=4: [order 35] for n>38
%F A301841 n=5: [order 99] for n>104
%e A301841 Some solutions for n=5 k=4
%e A301841 ..0..1..1..0. .0..1..0..1. .0..1..1..1. .0..0..0..0. .0..0..1..1
%e A301841 ..1..0..1..0. .1..1..0..1. .1..0..1..0. .1..1..0..1. .0..1..0..1
%e A301841 ..1..0..1..1. .1..0..1..0. .1..0..1..1. .0..1..0..1. .1..1..0..1
%e A301841 ..0..1..0..0. .0..0..1..0. .1..0..1..1. .0..0..1..0. .0..1..0..0
%e A301841 ..1..0..1..0. .0..1..0..1. .1..0..0..0. .1..1..0..1. .1..1..1..1
%Y A301841 Column 1 is A000079(n-1).
%Y A301841 Column 2 is A004171(n-1).
%Y A301841 Row 1 is A000079(n-1).
%K A301841 nonn,tabl
%O A301841 1,2
%A A301841 _R. H. Hardin_, Mar 27 2018