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A207067 Number of n X 7 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 0 1 and 1 0 1 vertically.

%I A207067 #8 Jun 18 2018 14:09:55
%S A207067 31,961,6634,27063,82739,210118,468348,947298,1776951,3138223,5275270,
%T A207067 8509345,13254267,20033564,29499352,42453012,59867727,82912941,
%U A207067 112980802,151714651,201039619,263195394,340771220,436743190,554513895,697954491
%N A207067 Number of n X 7 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 0 1 and 1 0 1 vertically.
%C A207067 Column 7 of A207068.
%H A207067 R. H. Hardin, <a href="/A207067/b207067.txt">Table of n, a(n) for n = 1..210</a>
%F A207067 Empirical: a(n) = (31/2520)*n^7 + (62/45)*n^6 + (4867/360)*n^5 + (2015/72)*n^4 + (1271/180)*n^3 - (4991/360)*n^2 - (713/140)*n.
%F A207067 Conjectures from _Colin Barker_, Jun 18 2018: (Start)
%F A207067 G.f.: 31*x*(1 + 23*x - 6*x^2 - 27*x^3 + 11*x^4) / (1 - x)^8.
%F A207067 a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.
%F A207067 (End)
%e A207067 Some solutions for n=4:
%e A207067 ..1..1..0..1..1..1..0....0..0..0..0..0..0..0....1..1..0..1..1..0..1
%e A207067 ..0..1..1..0..0..0..0....1..1..1..1..1..0..0....1..1..0..0..0..0..0
%e A207067 ..0..1..1..0..0..0..0....1..1..1..0..0..0..0....0..0..0..0..0..0..0
%e A207067 ..0..0..0..0..0..0..0....0..1..1..0..0..0..0....0..0..0..0..0..0..0
%Y A207067 Cf. A207068.
%K A207067 nonn
%O A207067 1,1
%A A207067 _R. H. Hardin_, Feb 14 2012