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A207064 Number of n X 4 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 0 1 and 1 0 1 vertically.

%I A207064 #10 Jun 18 2018 12:29:08
%S A207064 9,81,288,720,1485,2709,4536,7128,10665,15345,21384,29016,38493,50085,
%T A207064 64080,80784,100521,123633,150480,181440,216909,257301,303048,354600,
%U A207064 412425,477009,548856,628488,716445,813285,919584,1035936,1162953
%N A207064 Number of n X 4 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 0 1 and 1 0 1 vertically.
%C A207064 Column 4 of A207068.
%H A207064 R. H. Hardin, <a href="/A207064/b207064.txt">Table of n, a(n) for n = 1..210</a>
%F A207064 Empirical: a(n) = (3/4)*n^4 + (15/2)*n^3 + (15/4)*n^2 - 3*n.
%F A207064 Conjectures from _Colin Barker_, Jun 18 2018: (Start)
%F A207064 G.f.: 9*x*(1 + 4*x - 3*x^2) / (1 - x)^5.
%F A207064 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 A207064 (End)
%e A207064 Some solutions for n=4:
%e A207064 ..1..0..0..0....0..0..0..0....1..1..1..1....1..1..0..0....0..0..0..0
%e A207064 ..1..0..0..0....0..1..1..1....1..1..1..1....1..0..0..0....0..1..1..0
%e A207064 ..1..0..0..0....0..1..1..0....1..1..1..1....0..0..0..0....0..1..1..0
%e A207064 ..0..0..0..0....0..1..1..0....1..1..1..1....0..0..0..0....0..0..0..0
%Y A207064 Cf. A207068.
%K A207064 nonn
%O A207064 1,1
%A A207064 _R. H. Hardin_, Feb 14 2012