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A207065 Number of n X 5 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 0 1 and 1 0 1 vertically.

%I A207065 #8 Jun 18 2018 12:36:01
%S A207065 14,196,896,2688,6398,13132,24304,41664,67326,103796,154000,221312,
%T A207065 309582,423164,566944,746368,967470,1236900,1561952,1950592,2411486,
%U A207065 2954028,3588368,4325440,5176990,6155604,7274736,8548736,9992878
%N A207065 Number of n X 5 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 0 1 and 1 0 1 vertically.
%C A207065 Column 5 of A207068.
%H A207065 R. H. Hardin, <a href="/A207065/b207065.txt">Table of n, a(n) for n = 1..210</a>
%F A207065 Empirical: a(n) = (7/30)*n^5 + 7*n^4 + (21/2)*n^3 - (56/15)*n.
%F A207065 Conjectures from _Colin Barker_, Jun 18 2018: (Start)
%F A207065 G.f.: 14*x*(1 + 8*x - 5*x^2 - 2*x^3) / (1 - x)^6.
%F A207065 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 A207065 (End)
%e A207065 Some solutions for n=4:
%e A207065 ..0..1..1..1..0....0..0..0..0..0....1..1..0..0..0....1..0..1..1..0
%e A207065 ..0..1..1..0..1....1..1..0..0..0....0..1..1..1..1....1..1..0..0..0
%e A207065 ..0..0..0..0..0....1..1..0..0..0....0..1..1..0..1....0..0..0..0..0
%e A207065 ..0..0..0..0..0....1..0..0..0..0....0..1..1..0..0....0..0..0..0..0
%Y A207065 Cf. A207068.
%K A207065 nonn
%O A207065 1,1
%A A207065 _R. H. Hardin_, Feb 14 2012