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A295040 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 1 or 2 1s.

%I A295040 #6 Nov 23 2017 09:29:11
%S A295040 1,2,2,4,10,4,7,29,29,7,12,87,140,87,12,21,280,741,741,280,21,37,876,
%T A295040 3853,6686,3853,876,37,65,2735,19956,59126,59126,19956,2735,65,114,
%U A295040 8583,104096,528282,898493,528282,104096,8583,114,200,26900,541775,4738235
%N A295040 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 1 or 2 1s.
%C A295040 Table starts
%C A295040 ...1.....2.......4.........7..........12............21..............37
%C A295040 ...2....10......29........87.........280...........876............2735
%C A295040 ...4....29.....140.......741........3853.........19956..........104096
%C A295040 ...7....87.....741......6686.......59126........528282.........4738235
%C A295040 ..12...280....3853.....59126......898493......13706771.......209181266
%C A295040 ..21...876...19956....528282....13706771.....355281224......9248214732
%C A295040 ..37..2735..104096...4738235...209181266....9248214732....411280569141
%C A295040 ..65..8583..541775..42321441..3184995895..240292442848..18227207589288
%C A295040 .114.26900.2819027.378112132.48548926944.6243986963713.807975522778623
%H A295040 R. H. Hardin, <a href="/A295040/b295040.txt">Table of n, a(n) for n = 1..287</a>
%F A295040 Empirical for column k:
%F A295040 k=1: a(n) = 2*a(n-1) -a(n-2) +a(n-3)
%F A295040 k=2: a(n) = 2*a(n-1) +2*a(n-2) +5*a(n-3) -a(n-5) -a(n-6)
%F A295040 k=3: [order 15]
%F A295040 k=4: [order 34]
%F A295040 k=5: [order 91]
%e A295040 Some solutions for n=4 k=4
%e A295040 ..0..1..1..0. .0..0..0..0. .1..1..0..0. .0..1..0..0. .0..0..0..0
%e A295040 ..0..1..0..0. .1..0..0..1. .0..0..1..1. .0..1..0..0. .0..1..1..1
%e A295040 ..0..0..0..0. .1..1..0..1. .0..0..0..1. .0..0..0..1. .0..1..0..1
%e A295040 ..1..1..1..1. .0..1..1..0. .0..0..1..1. .0..0..0..1. .0..1..1..0
%Y A295040 Column 1 is A005251(n+2).
%Y A295040 Column 2 is A295525.
%K A295040 nonn,tabl
%O A295040 1,2
%A A295040 _R. H. Hardin_, Nov 12 2017