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A296952 T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 1, 3 or 5 king-move neighboring 1s.

%I A296952 #4 Dec 22 2017 11:10:30
%S A296952 1,2,2,3,8,3,4,16,16,4,6,36,45,36,6,9,112,135,135,112,9,13,256,544,
%T A296952 620,544,256,13,19,608,1765,3637,3637,1765,608,19,28,1680,5763,17450,
%U A296952 37179,17450,5763,1680,28,41,4064,20811,86139,256713,256713,86139,20811,4064
%N A296952 T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 1, 3 or 5 king-move neighboring 1s.
%C A296952 Table starts
%C A296952 ..1....2.....3.......4.........6..........9...........13............19
%C A296952 ..2....8....16......36.......112........256..........608..........1680
%C A296952 ..3...16....45.....135.......544.......1765.........5763.........20811
%C A296952 ..4...36...135.....620......3637......17450........86139........451210
%C A296952 ..6..112...544....3637.....37179.....256713......1898178......16087936
%C A296952 ..9..256..1765...17450....256713....2640993.....29067775.....356242817
%C A296952 .13..608..5763...86139...1898178...29067775....482228052....8786244680
%C A296952 .19.1680.20811..451210..16087936..356242817...8786244680..246430289779
%C A296952 .28.4064.70207.2267574.121741279.4007327435.148081034460.6194343019644
%H A296952 R. H. Hardin, <a href="/A296952/b296952.txt">Table of n, a(n) for n = 1..199</a>
%F A296952 Empirical for column k:
%F A296952 k=1: a(n) = a(n-1) +a(n-3)
%F A296952 k=2: a(n) = 2*a(n-1) +8*a(n-3) -12*a(n-4)
%F A296952 k=3: [order 19]
%F A296952 k=4: [order 46]
%e A296952 Some solutions for n=5 k=4
%e A296952 ..0..0..0..0. .0..1..0..0. .0..1..0..0. .0..0..0..0. .1..0..0..0
%e A296952 ..0..1..0..1. .0..1..0..0. .0..0..1..0. .0..0..0..0. .1..0..0..0
%e A296952 ..0..1..0..1. .0..0..0..1. .1..0..1..1. .0..0..0..1. .0..0..0..0
%e A296952 ..0..1..1..1. .0..0..0..1. .1..0..0..1. .0..1..1..0. .0..1..1..0
%e A296952 ..0..0..1..0. .0..0..0..0. .0..0..0..1. .0..0..0..1. .0..1..1..0
%Y A296952 Column 1 is A000930(n+1).
%K A296952 nonn,tabl
%O A296952 1,2
%A A296952 _R. H. Hardin_, Dec 22 2017