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A207597 Number of n X 6 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 1 0 1 vertically.

%I A207597 #8 Jun 25 2018 06:08:29
%S A207597 25,625,3025,9025,21025,42025,75625,126025,198025,297025,429025,
%T A207597 600625,819025,1092025,1428025,1836025,2325625,2907025,3591025,
%U A207597 4389025,5313025,6375625,7590025,8970025,10530025,12285025,14250625,16443025,18879025
%N A207597 Number of n X 6 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 1 0 1 vertically.
%C A207597 Column 6 of A207599.
%H A207597 R. H. Hardin, <a href="/A207597/b207597.txt">Table of n, a(n) for n = 1..210</a>
%F A207597 Empirical: a(n) = 25*n^4 + 50*n^3 - 25*n^2 - 50*n + 25.
%F A207597 Conjectures from _Colin Barker_, Jun 25 2018: (Start)
%F A207597 G.f.: 25*x*(1 + 20*x + 6*x^2 - 4*x^3 + x^4) / (1 - x)^5.
%F A207597 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 A207597 (End)
%e A207597 Some solutions for n=4:
%e A207597 ..0..1..1..0..1..1....1..1..1..1..1..1....1..0..1..1..1..1....0..0..1..1..0..0
%e A207597 ..1..1..1..1..0..1....0..0..1..1..1..1....0..0..1..1..0..0....0..0..1..1..1..1
%e A207597 ..1..0..1..1..0..0....0..0..1..1..0..0....0..0..1..1..0..0....0..0..1..1..0..0
%e A207597 ..0..0..1..1..0..0....0..0..1..1..0..0....0..0..1..1..0..0....0..0..1..1..0..0
%Y A207597 Cf. A207599.
%K A207597 nonn
%O A207597 1,1
%A A207597 _R. H. Hardin_, Feb 19 2012