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A295781 T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 0 or 2 king-move neighboring 1s.

%I A295781 #4 Nov 27 2017 07:15:52
%S A295781 2,3,3,5,9,5,8,19,19,8,13,49,56,49,13,21,123,198,198,123,21,34,297,
%T A295781 665,1059,665,297,34,55,739,2213,5263,5263,2213,739,55,89,1825,7479,
%U A295781 25529,37897,25529,7479,1825,89,144,4491,25105,127731,262707,262707,127731
%N A295781 T(n,k)=Number of nXk 0..1 arrays with each 1 adjacent to 0 or 2 king-move neighboring 1s.
%C A295781 Table starts
%C A295781 ..2....3.....5.......8.......13.........21..........34............55
%C A295781 ..3....9....19......49......123........297.........739..........1825
%C A295781 ..5...19....56.....198......665.......2213........7479.........25105
%C A295781 ..8...49...198....1059.....5263......25529......127731........630988
%C A295781 .13..123...665....5263....37897.....262707.....1905471......13577504
%C A295781 .21..297..2213...25529...262707....2602065....27085621.....276224518
%C A295781 .34..739..7479..127731..1905471...27085621...409525082....6037613762
%C A295781 .55.1825.25105..630988.13577504..276224518..6037613762..128171125105
%C A295781 .89.4491.84326.3118368.96726819.2819029784.89072774496.2722986415966
%H A295781 R. H. Hardin, <a href="/A295781/b295781.txt">Table of n, a(n) for n = 1..311</a>
%F A295781 Empirical for column k:
%F A295781 k=1: a(n) = a(n-1) +a(n-2)
%F A295781 k=2: a(n) = a(n-1) +2*a(n-2) +4*a(n-3)
%F A295781 k=3: a(n) = 2*a(n-1) +3*a(n-2) +6*a(n-3) -3*a(n-4) +2*a(n-5)
%F A295781 k=4: [order 10]
%F A295781 k=5: [order 22]
%F A295781 k=6: [order 43]
%F A295781 k=7: [order 91]
%e A295781 Some solutions for n=5 k=4
%e A295781 ..0..0..0..0. .0..0..0..0. .0..0..1..0. .0..0..0..1. .0..0..0..0
%e A295781 ..0..1..0..0. .0..0..0..1. .0..0..0..0. .1..1..0..0. .1..0..1..0
%e A295781 ..0..0..0..0. .0..0..0..0. .1..0..0..0. .1..0..0..1. .0..0..1..1
%e A295781 ..1..1..0..0. .1..1..0..0. .1..1..0..1. .0..0..1..1. .1..0..0..0
%e A295781 ..1..0..0..1. .0..1..0..0. .0..0..0..0. .0..0..0..0. .1..1..0..0
%Y A295781 Column 1 is A000045(n+2).
%Y A295781 Column 2 is A102001(n+1).
%K A295781 nonn,tabl
%O A295781 1,1
%A A295781 _R. H. Hardin_, Nov 27 2017