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A207257 Number of 6 X n 0..1 arrays avoiding 0 0 1 and 1 0 1 horizontally and 0 1 0 and 1 0 1 vertically.

%I A207257 #8 Jun 21 2018 10:47:43
%S A207257 26,676,4238,15652,43498,101036,207298,388232,677898,1119716,1767766,
%T A207257 2688140,3960346,5678764,7954154,10915216,14710202,19508580,25502750,
%U A207257 32909812,41973386,52965484,66188434,81976856,100699690,122762276
%N A207257 Number of 6 X n 0..1 arrays avoiding 0 0 1 and 1 0 1 horizontally and 0 1 0 and 1 0 1 vertically.
%C A207257 Row 6 of A207254.
%H A207257 R. H. Hardin, <a href="/A207257/b207257.txt">Table of n, a(n) for n = 1..210</a>
%F A207257 Empirical: a(n) = (13/180)*n^6 + (143/20)*n^5 + (1235/36)*n^4 - (39/4)*n^3 - (377/45)*n^2 + (13/5)*n.
%F A207257 Conjectures from _Colin Barker_, Jun 21 2018: (Start)
%F A207257 G.f.: 26*x*(1 + 19*x + 2*x^2 - 28*x^3 + 7*x^4 + x^5) / (1 - x)^7.
%F A207257 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) for n>7.
%F A207257 (End)
%e A207257 Some solutions for n=4:
%e A207257 ..1..1..1..1....0..1..1..1....1..0..0..0....0..1..0..0....1..1..0..0
%e A207257 ..1..1..1..1....1..1..0..0....1..1..0..0....1..0..0..0....1..0..0..0
%e A207257 ..1..1..1..1....1..1..0..0....0..1..0..0....1..0..0..0....1..0..0..0
%e A207257 ..1..1..1..0....1..0..0..0....0..0..0..0....1..0..0..0....1..1..1..1
%e A207257 ..1..0..0..0....0..0..0..0....0..0..0..0....0..1..1..0....0..1..1..1
%e A207257 ..1..0..0..0....0..1..1..0....0..0..0..0....0..1..1..0....0..0..0..0
%Y A207257 Cf. A207254.
%K A207257 nonn
%O A207257 1,1
%A A207257 _R. H. Hardin_, Feb 16 2012