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A207166 Number of n X 5 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 1 0 1 vertically.

%I A207166 #8 Jun 19 2018 12:33:24
%S A207166 13,169,624,1612,3445,6513,11284,18304,28197,41665,59488,82524,111709,
%T A207166 148057,192660,246688,311389,388089,478192,583180,704613,844129,
%U A207166 1003444,1184352,1388725,1618513,1875744,2162524,2481037,2833545,3222388,3649984
%N A207166 Number of n X 5 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 1 0 1 vertically.
%C A207166 Column 5 of A207169.
%H A207166 R. H. Hardin, <a href="/A207166/b207166.txt">Table of n, a(n) for n = 1..210</a>
%F A207166 Empirical: a(n) = (13/4)*n^4 + (13/2)*n^3 + (117/4)*n^2 - 26*n.
%F A207166 Conjectures from _Colin Barker_, Jun 19 2018: (Start)
%F A207166 G.f.: 13*x*(1 + 8*x - 7*x^2 + 4*x^3) / (1 - x)^5.
%F A207166 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 A207166 (End)
%e A207166 Some solutions for n=4:
%e A207166 ..1..1..1..1..0....1..1..0..0..1....1..0..0..1..0....1..1..1..0..0
%e A207166 ..1..1..1..1..1....0..0..1..1..0....1..1..1..0..0....0..1..1..1..1
%e A207166 ..1..1..1..1..1....0..0..1..0..0....0..0..1..0..0....0..1..1..1..0
%e A207166 ..1..1..0..0..1....0..0..1..0..0....0..0..1..0..0....0..0..1..1..0
%Y A207166 Cf. A207169.
%K A207166 nonn
%O A207166 1,1
%A A207166 _R. H. Hardin_, Feb 15 2012