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A207452 Number of n X 7 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 0 1 vertically.

%I A207452 #11 Jun 23 2018 05:49:28
%S A207452 42,1764,10710,36456,92610,196812,370734,640080,1034586,1588020,
%T A207452 2338182,3326904,4600050,6207516,8203230,10645152,13595274,17119620,
%U A207452 21288246,26175240,31858722,38420844,45947790,54529776,64261050,75239892,87568614
%N A207452 Number of n X 7 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 0 1 vertically.
%C A207452 Column 7 of A207453.
%H A207452 R. H. Hardin, <a href="/A207452/b207452.txt">Table of n, a(n) for n = 1..210</a>
%F A207452 Empirical: a(n) = 168*n^4 - 84*n^3 - 84*n^2 + 42*n.
%F A207452 Conjectures from _Colin Barker_, Jun 23 2018: (Start)
%F A207452 G.f.: 42*x*(1 + 37*x + 55*x^2 + 3*x^3) / (1 - x)^5.
%F A207452 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
%F A207452 (End)
%e A207452 Some solutions for n=5:
%e A207452   0 1 1 0 1 1 1      0 1 1 1 1 1 1      0 1 0 1 0 1 1
%e A207452   1 1 0 1 1 1 1      1 1 0 1 0 1 0      0 1 0 1 1 1 1
%e A207452   0 1 0 1 0 1 1      1 1 0 1 0 1 0      0 1 0 1 0 1 1
%e A207452   0 1 0 1 0 1 0      0 1 0 1 0 1 0      0 1 0 1 0 1 0
%e A207452   0 1 0 1 0 1 0      0 1 0 1 0 1 0      0 1 0 1 0 1 0
%Y A207452 Cf. A207453.
%K A207452 nonn
%O A207452 1,1
%A A207452 _R. H. Hardin_, Feb 17 2012