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A207390 Number of n X 7 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 0 1 and 1 1 0 vertically.

%I A207390 #9 Jun 22 2018 07:08:16
%S A207390 31,961,6115,23071,65955,158217,335915,651531,1178343,2015377,3292963,
%T A207390 5178919,7885387,11676345,16875819,23876819,33151023,45259233,
%U A207390 60862627,80734831,105774835,137020777,175664619,223067739,280777463,350544561
%N A207390 Number of n X 7 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 0 1 and 1 1 0 vertically.
%C A207390 Column 7 of A207391.
%H A207390 R. H. Hardin, <a href="/A207390/b207390.txt">Table of n, a(n) for n = 1..210</a>
%F A207390 Empirical: a(n) = (1/210)*n^7 + (103/180)*n^6 + (197/20)*n^5 + (1439/36)*n^4 + (293/20)*n^3 - (3469/90)*n^2 + (157/105)*n + 3.
%F A207390 Conjectures from _Colin Barker_, Jun 22 2018: (Start)
%F A207390 G.f.: x*(31 + 713*x - 705*x^2 - 677*x^3 + 961*x^4 - 341*x^5 + 45*x^6 - 3*x^7) / (1 - x)^8.
%F A207390 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 A207390 (End)
%e A207390 Some solutions for n=4:
%e A207390 ..0..1..1..1..1..0..0....0..1..1..1..0..0..0....1..1..0..1..1..0..1
%e A207390 ..0..1..1..1..0..0..0....0..0..0..0..0..0..0....1..1..0..0..0..0..0
%e A207390 ..0..1..1..1..1..0..0....0..0..0..0..0..0..0....1..1..0..1..1..0..1
%e A207390 ..0..1..1..1..1..0..0....0..0..0..0..0..0..0....1..1..0..1..1..0..1
%Y A207390 Cf. A207391.
%K A207390 nonn
%O A207390 1,1
%A A207390 _R. H. Hardin_, Feb 17 2012