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A207304 Number of n X 7 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 1 1 0 vertically.

%I A207304 #9 Jun 22 2018 07:08:36
%S A207304 28,784,4344,14446,36868,79802,154228,274288,457660,725932,1104976,
%T A207304 1625322,2322532,3237574,4417196,5914300,7788316,10105576,12939688,
%U A207304 16371910,20491524,25396210,31192420,37995752,45931324,55134148,65749504
%N A207304 Number of n X 7 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 1 1 0 vertically.
%C A207304 Column 7 of A207305.
%H A207304 R. H. Hardin, <a href="/A207304/b207304.txt">Table of n, a(n) for n = 1..210</a>
%F A207304 Empirical: a(n) = (187/60)*n^5 + (153/4)*n^4 + (455/12)*n^3 - (249/4)*n^2 + (209/30)*n + 4.
%F A207304 Conjectures from _Colin Barker_, Jun 22 2018: (Start)
%F A207304 G.f.: 2*x*(14 + 308*x + 30*x^2 - 209*x^3 + 46*x^4 - 2*x^5) / (1 - x)^6.
%F A207304 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 A207304 (End)
%e A207304 Some solutions for n=4:
%e A207304 ..1..1..0..0..1..1..1....0..0..1..0..0..1..1....0..1..0..0..1..0..0
%e A207304 ..0..0..1..1..1..0..0....1..1..1..1..0..0..1....1..0..0..1..1..1..1
%e A207304 ..1..0..0..1..1..1..1....0..1..1..0..0..1..1....1..0..0..1..1..1..0
%e A207304 ..0..0..1..1..1..1..1....1..1..1..1..0..0..1....1..0..0..1..1..1..0
%Y A207304 Cf. A207305.
%K A207304 nonn
%O A207304 1,1
%A A207304 _R. H. Hardin_, Feb 16 2012