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%I
%S 0,1,1,2,6,2,5,15,15,5,10,44,56,44,10,20,105,223,223,105,20,38,258,
%T 762,1148,762,258,38,71,595,2607,5170,5170,2607,595,71,130,1368,8500,
%U 23156,32056,23156,8500,1368,130,235,3069,27411,99057,193573,193573,99057
%N T(n,k)=Number of nXk binary arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two exactly once.
%C Table starts
%C ...0....1......2.......5........10.........20...........38............71
%C ...1....6.....15......44.......105........258..........595..........1368
%C ...2...15.....56.....223.......762.......2607.........8500.........27411
%C ...5...44....223....1148......5170......23156........99057........418924
%C ..10..105....762....5170.....32056.....193573......1129042.......6475898
%C ..20..258...2607...23156....193573....1552272.....12111209......92571436
%C ..38..595...8500...99057...1129042...12111209....127676872....1312123185
%C ..71.1368..27411..418924...6475898...92571436...1312123185...18045771274
%C .130.3069..86622.1736105..36505596..696659613..13311824510..245588158242
%C .235.6830.270955.7122856.203462597.5178525870.133228716170.3292985469950
%H R. H. Hardin, <a href="/A268766/b268766.txt">Table of n, a(n) for n = 1..1404</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4)
%F k=2: a(n) = 2*a(n-1) +3*a(n-2) -4*a(n-3) -4*a(n-4)
%F k=3: a(n) = 4*a(n-1) +2*a(n-2) -16*a(n-3) -a(n-4) +12*a(n-5) -4*a(n-6)
%F k=4: [order 8]
%F k=5: [order 12]
%F k=6: [order 16]
%F k=7: [order 28]
%e Some solutions for n=4 k=4
%e ..0..1..0..1. .1..0..0..0. .1..0..0..1. .0..0..0..1. .0..1..1..0
%e ..0..1..0..0. .0..0..0..1. .0..0..0..0. .0..0..0..1. .0..0..0..0
%e ..0..0..0..1. .0..1..0..0. .0..0..1..0. .0..0..0..0. .0..0..0..1
%e ..0..1..0..0. .0..1..0..0. .0..1..0..0. .1..0..0..1. .0..1..0..0
%Y Column 1 is A001629.
%Y Column 2 is A193449.
%K nonn,tabl
%O 1,4
%A _R. H. Hardin_, Feb 13 2016
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