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A207400 Number of n X 5 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 1 0 vertically.

%I A207400 #8 Jun 22 2018 08:27:43
%S A207400 12,144,612,1782,4212,8692,16284,28362,46652,73272,110772,162174,
%T A207400 231012,321372,437932,586002,771564,1001312,1282692,1623942,2034132,
%U A207400 2523204,3102012,3782362,4577052,5499912,6565844,7790862,9192132,10788012
%N A207400 Number of n X 5 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 1 0 vertically.
%C A207400 Column 5 of A207403.
%H A207400 R. H. Hardin, <a href="/A207400/b207400.txt">Table of n, a(n) for n = 1..210</a>
%F A207400 Empirical: a(n) = (1/3)*n^5 + 3*n^4 + (28/3)*n^3 + 7*n^2 - (29/3)*n + 2.
%F A207400 Conjectures from _Colin Barker_, Jun 22 2018: (Start)
%F A207400 G.f.: 2*x*(6 + 36*x - 36*x^2 + 15*x^3 - x^5) / (1 - x)^6.
%F A207400 a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.
%F A207400 (End)
%e A207400 Some solutions for n=4:
%e A207400 ..0..0..0..0..0....1..0..1..0..1....1..1..0..1..0....0..1..0..1..0
%e A207400 ..0..1..0..0..0....0..1..0..0..0....0..0..0..0..0....0..1..0..0..0
%e A207400 ..0..0..0..0..0....0..1..0..0..0....1..1..0..0..0....0..1..0..0..0
%e A207400 ..0..0..0..0..0....0..1..0..0..0....1..1..0..0..0....0..1..0..0..0
%Y A207400 Cf. A207403.
%K A207400 nonn
%O A207400 1,1
%A A207400 _R. H. Hardin_, Feb 17 2012