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A207701 Number of n X 6 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 1 1 0 vertically.

%I A207701 #9 Jun 25 2018 08:54:57
%S A207701 25,625,3969,15129,43681,105625,225625,439569,797449,1366561,2235025,
%T A207701 3515625,5349969,7912969,11417641,16120225,22325625,30393169,40742689,
%U A207701 53860921,70308225,90725625,115842169,146482609,183575401,228161025
%N A207701 Number of n X 6 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 1 1 0 vertically.
%C A207701 Column 6 of A207703.
%H A207701 R. H. Hardin, <a href="/A207701/b207701.txt">Table of n, a(n) for n = 1..210</a>
%F A207701 Empirical: a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7).
%F A207701 Conjectures from _Colin Barker_, Jun 25 2018: (Start)
%F A207701 G.f.: x*(25 + 450*x + 119*x^2 - 404*x^3 + 127*x^4 + 2*x^5 + x^6) / (1 - x)^7.
%F A207701 a(n) = (-3 + n + 15*n^2 + 2*n^3)^2 / 9.
%F A207701 (End)
%e A207701 Some solutions for n=4:
%e A207701 ..1..1..1..1..1..0....0..0..1..1..1..1....1..1..1..0..0..1....0..1..1..1..0..0
%e A207701 ..0..0..1..1..0..0....0..1..1..1..0..1....0..1..1..1..1..0....1..0..1..1..1..0
%e A207701 ..0..0..1..1..1..0....0..1..1..1..1..1....0..1..1..1..1..0....1..1..1..1..1..0
%e A207701 ..0..0..1..1..1..0....0..1..1..1..0..1....0..1..1..1..1..0....1..1..1..1..1..0
%Y A207701 Cf. A207703.
%K A207701 nonn
%O A207701 1,1
%A A207701 _R. H. Hardin_, Feb 19 2012