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%I #4 Dec 30 2017 07:01:07
%S 1,1,1,1,2,1,1,7,3,1,1,12,14,4,1,1,18,26,22,6,1,1,33,43,42,68,9,1,1,
%T 73,109,105,183,163,13,1,1,139,301,349,535,513,320,19,1,1,244,649,
%U 1057,2430,1673,1085,782,28,1,1,449,1332,2834,12005,11345,5108,3332,1889,41,1,1
%N T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 2 neighboring 1s.
%C Table starts
%C .1..1....1....1.....1.......1........1.........1..........1...........1
%C .1..2....7...12....18......33.......73.......139........244.........449
%C .1..3...14...26....43.....109......301.......649.......1332........3124
%C .1..4...22...42...105.....349.....1057......2834.......8216.......24556
%C .1..6...68..183...535....2430....12005.....45977.....182298......793315
%C .1..9..163..513..1673...11345....76692....369339....1884628....11192445
%C .1.13..320.1085..5108...50127...431723...2741816...19713343...158831909
%C .1.19..782.3332.19690..267505..3338387..28588498..275287217..3091469216
%C .1.28.1889.9744.66529.1348969.23694911.264853947.3362921639.52055334454
%H R. H. Hardin, <a href="/A297431/b297431.txt">Table of n, a(n) for n = 1..337</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)
%F k=2: a(n) = a(n-1) +a(n-3)
%F k=3: a(n) = a(n-1) +7*a(n-3) +a(n-5) -4*a(n-6)
%F k=4: a(n) = a(n-1) +12*a(n-3) +2*a(n-4) +2*a(n-5) -7*a(n-6) -a(n-7)
%F k=5: [order 20]
%F k=6: [order 37]
%F k=7: [order 81]
%F Empirical for row n:
%F n=1: a(n) = a(n-1)
%F n=2: a(n) = a(n-1) +a(n-3) +4*a(n-4)
%F n=3: a(n) = a(n-1) +3*a(n-3) +8*a(n-4) +a(n-5) -a(n-6)
%F n=4: [order 12]
%F n=5: [order 29]
%F n=6: [order 59]
%e Some solutions for n=5 k=4
%e ..0..0..1..1. .0..1..1..1. .0..0..1..1. .0..0..0..0. .0..0..0..0
%e ..0..0..1..1. .0..0..1..0. .0..0..1..1. .0..0..0..0. .0..0..1..0
%e ..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..1..1. .0..1..0..1
%e ..0..1..1..1. .0..1..1..0. .1..1..0..0. .0..1..1..0. .0..0..1..0
%e ..0..0..1..0. .1..1..0..0. .1..1..0..0. .0..0..0..0. .0..0..0..0
%Y Column 2 is A000930(n+1).
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Dec 30 2017
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