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%I #4 Dec 01 2014 11:33:38
%S 9,22,22,52,71,52,125,219,219,125,297,701,822,701,297,710,2193,3390,
%T 3390,2193,710,1691,6980,12954,18924,12954,6980,1691,4036,21966,52474,
%U 94706,94706,52474,21966,4036,9621,69681,202882,518711,577942,518711,202882
%N T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with every 2X2 subblock having a single 1 or two 1s on the same edge or main diagonally
%C Table starts
%C .....9.....22.......52.......125........297..........710..........1691
%C ....22.....71......219.......701.......2193.........6980.........21966
%C ....52....219......822......3390......12954........52474........202882
%C ...125....701.....3390.....18924......94706.......518711.......2645966
%C ...297...2193....12954.....94706.....577942......4109933......25654154
%C ...710...6980....52474....518711....4109933.....39473392.....322933003
%C ..1691..21966...202882...2645966...25654154....322933003....3232216177
%C ..4036..69681...813336..14292754..178853600...3029148345...39571705178
%C ..9621.219860..3168621..73763850.1134888362..25329125380..405845538185
%C .22951.696284.12623928.394839392.7800498387.233446638426.4863503527792
%H R. H. Hardin, <a href="/A251292/b251292.txt">Table of n, a(n) for n = 1..544</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1) +2*a(n-2) -3*a(n-3) +a(n-4)
%F k=2: a(n) = 2*a(n-1) +7*a(n-2) -9*a(n-3) -7*a(n-4) +7*a(n-5) for n>6
%F k=3: [order 11]
%F k=4: [order 19]
%F k=5: [order 33] for n>34
%F k=6: [order 58] for n>59
%e Some solutions for n=4 k=4
%e ..0..0..0..0..0....1..1..1..1..1....0..1..0..0..0....1..0..0..0..0
%e ..1..1..0..1..1....0..0..0..0..0....0..0..1..0..1....0..1..1..1..1
%e ..0..0..0..0..0....1..0..1..1..0....1..0..1..0..1....0..0..0..0..0
%e ..0..1..0..1..1....1..0..0..0..1....1..0..0..0..1....1..1..0..1..0
%e ..0..1..0..0..0....0..1..1..0..0....1..0..1..0..0....0..0..0..0..1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 01 2014
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