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A295416 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 1, 2 or 3 1s.

%I A295416 #4 Nov 22 2017 10:40:16
%S A295416 1,2,2,4,10,4,7,36,36,7,12,126,234,126,12,21,454,1534,1534,454,21,37,
%T A295416 1632,10291,19026,10291,1632,37,65,5854,68613,240439,240439,68613,
%U A295416 5854,65,114,21010,457178,3019079,5741797,3019079,457178,21010,114,200,75412
%N A295416 T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 1, 2 or 3 1s.
%C A295416 Table starts
%C A295416 ...1.....2........4..........7............12..............21.................37
%C A295416 ...2....10.......36........126...........454............1632...............5854
%C A295416 ...4....36......234.......1534.........10291...........68613.............457178
%C A295416 ...7...126.....1534......19026........240439.........3019079...........37927609
%C A295416 ..12...454....10291.....240439.......5741797.......136204120.........3232240913
%C A295416 ..21..1632....68613....3019079.....136204120......6093564449.......272714953724
%C A295416 ..37..5854...457178...37927609....3232240913....272714953724.....23025368248778
%C A295416 ..65.21010..3048314..476686533...76727059034..12210363190599...1945003010538968
%C A295416 .114.75412.20323497.5990217198.1821136011730.546643613178667.164274708080518128
%H A295416 R. H. Hardin, <a href="/A295416/b295416.txt">Table of n, a(n) for n = 1..312</a>
%F A295416 Empirical for column k:
%F A295416 k=1: a(n) = 2*a(n-1) -a(n-2) +a(n-3)
%F A295416 k=2: a(n) = 3*a(n-1) +a(n-2) +4*a(n-3)
%F A295416 k=3: a(n) = 6*a(n-1) +28*a(n-3) +3*a(n-4) +49*a(n-5) +33*a(n-6) -34*a(n-7) -22*a(n-8)
%F A295416 k=4: [order 14]
%F A295416 k=5: [order 37]
%F A295416 k=6: [order 78]
%e A295416 Some solutions for n=5 k=4
%e A295416 ..0..0..0..0. .0..1..1..0. .0..1..0..1. .0..1..0..0. .0..0..1..1
%e A295416 ..1..0..1..1. .0..0..1..0. .0..1..1..1. .0..1..0..0. .1..1..1..1
%e A295416 ..1..1..1..0. .1..1..0..1. .0..1..0..1. .1..0..0..1. .0..0..0..1
%e A295416 ..0..1..0..0. .1..0..0..1. .1..1..0..1. .1..1..0..1. .0..0..1..1
%e A295416 ..0..0..1..1. .0..0..1..1. .1..1..1..1. .1..1..1..0. .0..1..1..1
%Y A295416 Column 1 is A005251(n+2).
%Y A295416 Column 2 is A202796.
%K A295416 nonn,tabl
%O A295416 1,2
%A A295416 _R. H. Hardin_, Nov 22 2017