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A295120 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 1 or 4 1s.

%I A295120 #4 Nov 15 2017 06:21:58
%S A295120 1,2,2,3,5,3,4,9,9,4,6,20,26,20,6,9,41,77,77,41,9,13,85,226,326,226,
%T A295120 85,13,19,178,665,1373,1373,665,178,19,28,369,1960,5793,8257,5793,
%U A295120 1960,369,28,41,769,5769,24347,49302,49302,24347,5769,769,41,60,1600,16983,102398
%N A295120 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 1 or 4 1s.
%C A295120 Table starts
%C A295120 ..1...2.....3......4........6.........9.........13...........19............28
%C A295120 ..2...5.....9.....20.......41........85........178..........369...........769
%C A295120 ..3...9....26.....77......226.......665.......1960.........5769.........16983
%C A295120 ..4..20....77....326.....1373......5793......24347.......102398........431050
%C A295120 ..6..41...226...1373.....8257.....49302.....295083......1768323......10586331
%C A295120 ..9..85...665...5793....49302....420519....3590821.....30650456.....261518933
%C A295120 .13.178..1960..24347...295083...3590821...43655680....530696748....6452840307
%C A295120 .19.369..5769.102398..1768323..30650456..530696748...9196006628..159316011413
%C A295120 .28.769.16983.431050.10586331.261518933.6452840307.159316011413.3931962260999
%H A295120 R. H. Hardin, <a href="/A295120/b295120.txt">Table of n, a(n) for n = 1..391</a>
%F A295120 Empirical for column k:
%F A295120 k=1: a(n) = a(n-1) +a(n-3)
%F A295120 k=2: a(n) = a(n-1) +2*a(n-2) +a(n-3) -a(n-4)
%F A295120 k=3: [order 10]
%F A295120 k=4: [order 14]
%F A295120 k=5: [order 40]
%F A295120 k=6: [order 78]
%e A295120 Some solutions for n=5 k=4
%e A295120 ..0..1..0..0. .0..1..0..0. .0..0..0..0. .1..0..0..0. .1..1..0..0
%e A295120 ..0..1..0..0. .1..1..1..0. .0..1..1..0. .1..0..1..1. .0..0..0..0
%e A295120 ..1..0..0..0. .0..1..0..0. .0..0..0..1. .0..0..0..0. .0..0..1..0
%e A295120 ..1..0..0..1. .1..0..1..0. .0..0..0..1. .0..0..0..0. .0..0..1..0
%e A295120 ..0..0..0..1. .1..0..1..0. .0..1..1..0. .1..1..0..0. .0..0..0..0
%Y A295120 Column 1 is A000930(n+1).
%Y A295120 Column 2 is A105309(n+1).
%K A295120 nonn,tabl
%O A295120 1,2
%A A295120 _R. H. Hardin_, Nov 15 2017