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A207256 Number of 5 X n 0..1 arrays avoiding 0 0 1 and 1 0 1 horizontally and 0 1 0 and 1 0 1 vertically.

%I A207256 #8 Jun 21 2018 10:31:50
%S A207256 16,256,1232,3776,9072,18688,34608,59264,95568,146944,217360,311360,
%T A207256 434096,591360,789616,1036032,1338512,1705728,2147152,2673088,3294704,
%U A207256 4024064,4874160,5858944,6993360,8293376,9776016,11459392,13362736
%N A207256 Number of 5 X n 0..1 arrays avoiding 0 0 1 and 1 0 1 horizontally and 0 1 0 and 1 0 1 vertically.
%C A207256 Row 5 of A207254.
%H A207256 R. H. Hardin, <a href="/A207256/b207256.txt">Table of n, a(n) for n = 1..210</a>
%F A207256 Empirical: a(n) = (4/15)*n^5 + (32/3)*n^4 + (44/3)*n^3 - (32/3)*n^2 + (16/15)*n.
%F A207256 Conjectures from _Colin Barker_, Jun 21 2018: (Start)
%F A207256 G.f.: 16*x*(1 + 10*x - 4*x^2 - 6*x^3 + x^4) / (1 - x)^6.
%F A207256 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 A207256 (End)
%e A207256 Some solutions for n=4:
%e A207256 ..1..0..0..0....0..1..1..0....0..1..0..0....0..1..1..0....1..1..1..1
%e A207256 ..0..1..1..0....1..1..0..0....1..1..1..0....0..1..1..1....1..1..0..0
%e A207256 ..0..1..1..1....1..0..0..0....1..1..1..1....1..1..1..1....0..0..0..0
%e A207256 ..1..1..1..1....0..0..0..0....0..1..1..1....1..0..0..0....0..0..0..0
%e A207256 ..1..1..0..0....0..0..0..0....0..0..0..0....1..0..0..0....1..0..0..0
%Y A207256 Cf. A207254.
%K A207256 nonn
%O A207256 1,1
%A A207256 _R. H. Hardin_, Feb 16 2012