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A296327 T(n,k) = Number of n X k 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 2 neighboring 1's.

%I A296327 #6 May 24 2024 15:57:11
%S A296327 1,1,1,1,3,1,1,5,5,1,1,8,11,8,1,1,15,23,23,15,1,1,26,54,61,54,26,1,1,
%T A296327 45,122,185,185,122,45,1,1,80,278,562,853,562,278,80,1,1,140,634,1677,
%U A296327 3569,3569,1677,634,140,1,1,245,1438,4998,14691,20088,14691,4998,1438,245,1,1
%N A296327 T(n,k) = Number of n X k 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 2 neighboring 1's.
%C A296327 Table starts
%C A296327 .1...1....1.....1......1.......1........1.........1...........1............1
%C A296327 .1...3....5.....8.....15......26.......45........80.........140..........245
%C A296327 .1...5...11....23.....54.....122......278.......634........1438.........3274
%C A296327 .1...8...23....61....185.....562.....1677......4998.......14968........44818
%C A296327 .1..15...54...185....853....3569....14691.....62193......261763......1099727
%C A296327 .1..26..122...562...3569...20088...112235....643541.....3666933.....20890748
%C A296327 .1..45..278..1677..14691..112235...850404...6660799....51754039....401363520
%C A296327 .1..80..634..4998..62193..643541..6660799..72224019...769931084...8196375877
%C A296327 .1.140.1438.14968.261763.3666933.51754039.769931084.11207386103.163095751500
%H A296327 R. H. Hardin, <a href="/A296327/b296327.txt">Table of n, a(n) for n = 1..449</a>
%F A296327 Empirical for column k:
%F A296327 k=1: a(n) = a(n-1).
%F A296327 k=2: a(n) = a(n-1) +2*a(n-3) +a(n-5).
%F A296327 k=3: a(n) = 2*a(n-1) -a(n-2) +4*a(n-3) -2*a(n-4) +4*a(n-5) -3*a(n-6) +2*a(n-7) -a(n-8).
%F A296327 k=4: [order 14].
%F A296327 k=5: [order 40].
%F A296327 k=6: [order 83].
%e A296327 Some solutions for n=5, k=4
%e A296327 ..1..1..0..0. .1..1..0..1. .0..0..0..0. .0..1..1..0. .0..1..0..0
%e A296327 ..1..0..0..0. .1..0..1..1. .0..0..0..0. .0..1..0..0. .1..1..0..0
%e A296327 ..0..0..0..0. .0..0..0..0. .0..0..1..1. .0..0..0..0. .0..0..0..0
%e A296327 ..0..0..1..1. .0..0..1..0. .0..1..0..1. .0..0..0..1. .1..1..0..1
%e A296327 ..0..0..1..0. .0..1..1..0. .0..1..1..0. .0..0..1..1. .1..0..1..1
%Y A296327 Column 2 is A193147(n+1).
%K A296327 nonn,tabl
%O A296327 1,5
%A A296327 _R. H. Hardin_, Dec 10 2017