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A297654 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1, 2 or 3 neighboring 1s.

%I A297654 #4 Jan 02 2018 15:14:40
%S A297654 1,2,1,4,10,1,7,43,36,1,12,140,231,126,1,21,494,1073,1421,454,1,37,
%T A297654 1845,6838,11024,9033,1632,1,65,6757,45036,131044,113252,55706,5854,1,
%U A297654 114,24479,268655,1580681,2525244,1105531,346032,21010,1,200,89068,1617465
%N A297654 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1, 2 or 3 neighboring 1s.
%C A297654 Table starts
%C A297654 .1.....2........4..........7...........12.............21................37
%C A297654 .1....10.......43........140..........494...........1845..............6757
%C A297654 .1....36......231.......1073.........6838..........45036............268655
%C A297654 .1...126.....1421......11024.......131044........1580681..........16899640
%C A297654 .1...454.....9033.....113252......2525244.......56630842........1075678445
%C A297654 .1..1632....55706....1105531.....46187510.....1906300826.......63350980838
%C A297654 .1..5854...346032...11089103....864944851....65775301075.....3863740405975
%C A297654 .1.21010..2151932..110654243..16149058068..2265577299182...234680441414485
%C A297654 .1.75412.13364992.1101808354.300870617401.77814433907002.14203234114710492
%H A297654 R. H. Hardin, <a href="/A297654/b297654.txt">Table of n, a(n) for n = 1..219</a>
%F A297654 Empirical for column k:
%F A297654 k=1: a(n) = a(n-1)
%F A297654 k=2: a(n) = 3*a(n-1) +a(n-2) +4*a(n-3)
%F A297654 k=3: [order 11]
%F A297654 k=4: [order 24]
%F A297654 k=5: [order 60]
%F A297654 Empirical for row n:
%F A297654 n=1: a(n) = 2*a(n-1) -a(n-2) +a(n-3)
%F A297654 n=2: a(n) = 3*a(n-1) -2*a(n-2) +13*a(n-3) +6*a(n-4) +12*a(n-5) +12*a(n-6)
%F A297654 n=3: [order 17]
%F A297654 n=4: [order 38]
%e A297654 Some solutions for n=4 k=4
%e A297654 ..0..1..1..0. .0..0..0..1. .0..1..1..0. .0..0..1..0. .1..1..1..1
%e A297654 ..0..0..0..0. .0..0..1..1. .0..0..0..1. .1..0..0..1. .0..0..0..1
%e A297654 ..1..1..1..1. .0..0..0..0. .1..1..0..0. .0..1..1..0. .1..1..0..0
%e A297654 ..0..1..0..0. .0..0..1..1. .1..1..0..0. .1..0..0..0. .1..1..1..0
%Y A297654 Column 2 is A202796.
%Y A297654 Row 1 is A005251(n+2).
%K A297654 nonn,tabl
%O A297654 1,2
%A A297654 _R. H. Hardin_, Jan 02 2018