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A207937 Number of n X 7 0..1 arrays avoiding 0 0 1 and 1 0 0 horizontally and 0 0 1 and 1 1 0 vertically.

%I A207937 #8 Jun 26 2018 09:13:28
%S A207937 35,1225,8977,38207,121313,319439,737575,1544037,2994871,5463725,
%T A207937 9477733,15759955,25278917,39305795,59479787,87882217,127119915,
%U A207937 180418417,251725529,345825799,468466441,626495255,828011087,1082527373,1401149311
%N A207937 Number of n X 7 0..1 arrays avoiding 0 0 1 and 1 0 0 horizontally and 0 0 1 and 1 1 0 vertically.
%C A207937 Column 7 of A207938.
%H A207937 R. H. Hardin, <a href="/A207937/b207937.txt">Table of n, a(n) for n = 1..210</a>
%F A207937 Empirical: 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).
%F A207937 Conjectures from _Colin Barker_, Jun 26 2018: (Start)
%F A207937 G.f.: x*(35 + 945*x + 157*x^2 - 1269*x^3 + 863*x^4 - 191*x^5 + 5*x^6 - x^7) / (1 - x)^8.
%F A207937 a(n) = (1260 + 4974*n - 32165*n^2 - 6041*n^3 + 51940*n^4 + 21091*n^5 + 2905*n^6 + 136*n^7) / 1260.
%F A207937 (End)
%e A207937 Some solutions for n=4:
%e A207937 ..1..0..1..0..1..0..1....1..0..1..0..1..1..0....1..1..1..1..1..1..1
%e A207937 ..1..1..0..1..0..1..0....1..1..1..1..0..1..0....0..1..1..1..1..0..1
%e A207937 ..1..0..1..0..1..1..0....1..0..1..0..1..1..0....1..1..1..1..1..1..1
%e A207937 ..1..0..1..1..1..1..0....1..0..1..1..1..1..0....0..1..1..1..1..0..1
%Y A207937 Cf. A207938.
%K A207937 nonn
%O A207937 1,1
%A A207937 _R. H. Hardin_, Feb 21 2012