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A208284 Number of n X 5 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 1 0 vertically.

%I A208284 #8 Jun 29 2018 11:37:46
%S A208284 16,256,1260,3984,9900,21096,40376,71360,118584,187600,285076,418896,
%T A208284 598260,833784,1137600,1523456,2006816,2604960,3337084,4224400,
%U A208284 5290236,6560136,8061960,9825984,11885000,14274416,17032356,20199760,23820484
%N A208284 Number of n X 5 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 1 0 vertically.
%C A208284 Column 5 of A208287.
%H A208284 R. H. Hardin, <a href="/A208284/b208284.txt">Table of n, a(n) for n = 1..210</a>
%F A208284 Empirical: a(n) = (5/6)*n^5 + 9*n^4 + (91/6)*n^3 - 9*n^2.
%F A208284 Conjectures from _Colin Barker_, Jun 29 2018: (Start)
%F A208284 G.f.: 4*x*(2 - x)*(2 + 21*x + 6*x^2 - 4*x^3) / (1 - x)^6.
%F A208284 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 A208284 (End)
%e A208284 Some solutions for n=4:
%e A208284 ..0..1..0..1..0....0..1..0..1..0....0..1..0..1..1....1..0..1..1..1
%e A208284 ..1..0..1..0..0....1..1..0..1..1....0..1..0..1..0....0..1..0..1..1
%e A208284 ..1..1..0..1..0....1..1..0..1..0....0..1..0..1..0....0..1..1..1..1
%e A208284 ..1..1..0..1..0....1..1..0..1..0....0..1..0..1..0....0..1..1..1..1
%Y A208284 Cf. A208287.
%K A208284 nonn
%O A208284 1,1
%A A208284 _R. H. Hardin_, Feb 25 2012