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A295531 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 1, 2 or 4 1s.

%I A295531 #4 Nov 23 2017 09:27:46
%S A295531 1,2,2,4,10,4,7,29,29,7,12,87,147,87,12,21,280,774,774,280,21,37,876,
%T A295531 4080,7071,4080,876,37,65,2735,21489,64189,64189,21489,2735,65,114,
%U A295531 8583,113466,588529,1012315,588529,113466,8583,114,200,26900,598374,5400933
%N A295531 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 1, 2 or 4 1s.
%C A295531 Table starts
%C A295531 ...1.....2.......4.........7..........12............21...............37
%C A295531 ...2....10......29........87.........280...........876.............2735
%C A295531 ...4....29.....147.......774........4080.........21489...........113466
%C A295531 ...7....87.....774......7071.......64189........588529..........5400933
%C A295531 ..12...280....4080.....64189.....1012315......16031147........253594307
%C A295531 ..21...876...21489....588529....16031147.....437241277......11938414614
%C A295531 ..37..2735..113466...5400933...253594307...11938414614.....563330031268
%C A295531 ..65..8583..598374..49414072..4003959566..325438086413...26515589323171
%C A295531 .114.26900.3155426.452274232.63279327977.8875686431050.1248681784524804
%H A295531 R. H. Hardin, <a href="/A295531/b295531.txt">Table of n, a(n) for n = 1..241</a>
%F A295531 Empirical for column k:
%F A295531 k=1: a(n) = 2*a(n-1) -a(n-2) +a(n-3)
%F A295531 k=2: a(n) = 2*a(n-1) +2*a(n-2) +5*a(n-3) -a(n-5) -a(n-6)
%F A295531 k=3: [order 18]
%F A295531 k=4: [order 45]
%e A295531 Some solutions for n=5 k=4
%e A295531 ..0..1..1..1. .1..1..0..1. .0..0..1..1. .1..1..1..0. .0..1..1..0
%e A295531 ..0..1..0..1. .1..0..0..1. .0..0..0..1. .0..0..0..1. .0..0..0..0
%e A295531 ..1..1..0..0. .0..1..1..0. .1..0..0..1. .1..1..0..1. .1..1..0..0
%e A295531 ..0..0..1..1. .1..1..1..0. .1..0..0..0. .1..0..0..1. .0..1..0..1
%e A295531 ..0..0..1..1. .1..1..0..0. .0..1..1..0. .1..1..1..0. .0..1..1..1
%Y A295531 Column 1 is A005251(n+2).
%K A295531 nonn,tabl
%O A295531 1,2
%A A295531 _R. H. Hardin_, Nov 23 2017