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A268789 T(n,k)=Number of nXk binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two exactly once.

%I A268789 #4 Feb 13 2016 12:26:53
%S A268789 0,1,1,2,5,2,5,17,17,5,10,48,72,48,10,20,131,302,302,131,20,38,338,
%T A268789 1144,1714,1144,338,38,71,850,4207,9085,9085,4207,850,71,130,2091,
%U A268789 14984,46195,67100,46195,14984,2091,130,235,5061,52335,228384,477128,477128,228384
%N A268789 T(n,k)=Number of nXk binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two exactly once.
%C A268789 Table starts
%C A268789 ...0.....1......2........5........10..........20............38.............71
%C A268789 ...1.....5.....17.......48.......131.........338...........850...........2091
%C A268789 ...2....17.....72......302......1144........4207.........14984..........52335
%C A268789 ...5....48....302.....1714......9085.......46195........228384........1105510
%C A268789 ..10...131...1144.....9085.....67100......477128.......3295246.......22302699
%C A268789 ..20...338...4207....46195....477128.....4725018......45515227......429442918
%C A268789 ..38...850..14984...228384...3295246....45515227.....611932378.....8057509992
%C A268789 ..71..2091..52335..1105510..22302699...429442918....8057509992...148013550916
%C A268789 .130..5061.179854..5267662.148575958..3988796543..104456486696..2677312316674
%C A268789 .235.12095.610504.24786180.977609634.36591758790.1337467436839.47829470133134
%H A268789 R. H. Hardin, <a href="/A268789/b268789.txt">Table of n, a(n) for n = 1..1404</a>
%F A268789 Empirical for column k:
%F A268789 k=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4)
%F A268789 k=2: a(n) = 2*a(n-1) +3*a(n-2) -2*a(n-3) -6*a(n-4) -4*a(n-5) -a(n-6)
%F A268789 k=3: [order 10]
%F A268789 k=4: [order 16]
%F A268789 k=5: [order 26]
%F A268789 k=6: [order 42]
%F A268789 k=7: [order 68]
%e A268789 Some solutions for n=4 k=4
%e A268789 ..0..0..0..0. .1..0..1..0. .1..0..1..0. .1..1..0..0. .1..1..0..0
%e A268789 ..1..0..1..0. .0..0..0..0. .0..1..0..0. .0..0..0..0. .0..0..0..1
%e A268789 ..0..0..0..1. .1..0..0..1. .0..0..0..1. .0..0..0..1. .0..0..0..0
%e A268789 ..0..1..0..1. .0..0..1..0. .1..0..0..0. .0..0..0..0. .1..0..0..0
%Y A268789 Column 1 is A001629.
%K A268789 nonn,tabl
%O A268789 1,4
%A A268789 _R. H. Hardin_, Feb 13 2016