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A209647 Number of n X 5 0..1 arrays avoiding 0 0 1 and 1 0 0 horizontally and 0 0 1 and 1 0 1 vertically.

%I A209647 #13 Mar 08 2018 02:48:36
%S A209647 14,196,798,2156,4690,8904,15386,24808,37926,55580,78694,108276,
%T A209647 145418,191296,247170,314384,394366,488628,598766,726460,873474,
%U A209647 1041656,1232938,1449336,1692950,1965964,2270646,2609348,2984506,3398640,3854354,4354336
%N A209647 Number of n X 5 0..1 arrays avoiding 0 0 1 and 1 0 0 horizontally and 0 0 1 and 1 0 1 vertically.
%C A209647 Column 5 of A209650.
%H A209647 R. H. Hardin, <a href="/A209647/b209647.txt">Table of n, a(n) for n = 1..210</a>
%H A209647 Robert Israel, <a href="/A209647/a209647.pdf">Maple-assisted proof of formula</a>
%F A209647 Empirical: a(n) = (7/2)*n^4 + 21*n^3 - (7/2)*n^2 - 7*n.
%F A209647 Conjectures from _Colin Barker_, Mar 07 2018: (Start)
%F A209647 G.f.: 14*x*(1 + 9*x - 3*x^2 - x^3) / (1 - x)^5.
%F A209647 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
%F A209647 (End)
%F A209647 Empirical formula (and thus Barker's conjectures) proved by _Robert Israel_, Mar 07 2018: see link.
%e A209647 Some solutions for n=4:
%e A209647   0 0 0 0 0    0 1 1 1 1    1 1 0 1 0    0 1 0 1 0
%e A209647   1 0 1 0 1    1 1 0 1 1    0 1 1 1 1    1 1 1 0 1
%e A209647   1 0 1 0 1    0 1 0 1 0    0 0 0 0 0    0 0 0 0 0
%e A209647   0 0 0 0 0    0 0 0 0 0    0 0 0 0 0    0 0 0 0 0
%p A209647 seq(7/2*n^4+21*n^3-7/2*n^2-7*n, n=1..50); # _Robert Israel_, Mar 07 2018
%Y A209647 Cf. A209650.
%K A209647 nonn
%O A209647 1,1
%A A209647 _R. H. Hardin_, Mar 11 2012