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A209649 Number of n X 7 0..1 arrays avoiding 0 0 1 and 1 0 0 horizontally and 0 0 1 and 1 0 1 vertically.

%I A209649 #12 Mar 09 2018 10:54:46
%S A209649 35,1225,7210,24990,65765,145775,287140,518700,876855,1406405,2161390,
%T A209649 3205930,4615065,6475595,8886920,11961880,15827595,20626305,26516210,
%U A209649 33672310,42287245,52572135,64757420,79093700,95852575,115327485
%N A209649 Number of n X 7 0..1 arrays avoiding 0 0 1 and 1 0 0 horizontally and 0 0 1 and 1 0 1 vertically.
%C A209649 Column 7 of A209650.
%H A209649 R. H. Hardin, <a href="/A209649/b209649.txt">Table of n, a(n) for n = 1..210</a>
%F A209649 Empirical: a(n) = 7*n^5 + 70*n^4 + (35/3)*n^3 - (105/2)*n^2 - (7/6)*n.
%F A209649 Conjectures from _Colin Barker_, Mar 07 2018: (Start)
%F A209649 G.f.: 35*x*(1 + x)*(1 + 28*x - 17*x^2) / (1 - x)^6.
%F A209649 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 A209649 (End)
%e A209649 Some solutions for n=4:
%e A209649   1 0 1 0 1 0 1     0 1 0 1 1 1 0     1 1 0 1 1 0 1
%e A209649   0 0 0 0 0 0 0     0 0 0 0 0 0 0     0 0 0 0 0 0 0
%e A209649   0 0 0 0 0 0 0     0 0 0 0 0 0 0     0 0 0 0 0 0 0
%e A209649   0 0 0 0 0 0 0     0 0 0 0 0 0 0     0 0 0 0 0 0 0
%Y A209649 Cf. A209650.
%K A209649 nonn
%O A209649 1,1
%A A209649 _R. H. Hardin_, Mar 11 2012