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A207109 Number of n X 6 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 0 1 and 1 1 0 vertically.

%I A207109 #9 Jun 19 2018 03:32:51
%S A207109 18,324,1504,4534,10898,22714,42874,75198,124602,197280,300900,444814,
%T A207109 640282,900710,1241902,1682326,2243394,2949756,3829608,4915014,
%U A207109 6242242,7852114,9790370,12108046,14861866,18114648,21935724,26401374,31595274
%N A207109 Number of n X 6 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 0 1 and 1 1 0 vertically.
%C A207109 Column 6 of A207111.
%H A207109 R. H. Hardin, <a href="/A207109/b207109.txt">Table of n, a(n) for n = 1..210</a>
%F A207109 Empirical: a(n) = (7/360)*n^6 + (77/120)*n^5 + (635/72)*n^4 + (623/24)*n^3 - (511/180)*n^2 - (103/5)*n + 6.
%F A207109 Conjectures from _Colin Barker_, Jun 19 2018: (Start)
%F A207109 G.f.: 2*x*(9 + 99*x - 193*x^2 + 90*x^3 + 17*x^4 - 18*x^5 + 3*x^6) / (1 - x)^7.
%F A207109 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 A207109 (End)
%e A207109 Some solutions for n=4:
%e A207109 ..0..0..1..0..1..0....1..1..1..1..1..0....1..1..0..0..1..0....0..1..0..1..0..0
%e A207109 ..0..1..0..1..0..1....0..0..1..0..0..1....1..0..1..0..0..1....1..0..1..0..1..0
%e A207109 ..0..1..0..0..1..0....0..0..1..0..1..0....1..1..1..0..0..1....1..1..0..0..1..0
%e A207109 ..0..1..0..0..1..0....0..0..1..0..1..0....1..1..1..0..0..1....1..1..1..0..1..0
%Y A207109 Cf. A207111.
%K A207109 nonn
%O A207109 1,1
%A A207109 _R. H. Hardin_, Feb 15 2012