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A207165 Number of n X 4 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 1 0 1 vertically.

%I A207165 #8 Jun 19 2018 12:28:19
%S A207165 9,81,261,603,1161,1989,3141,4671,6633,9081,12069,15651,19881,24813,
%T A207165 30501,36999,44361,52641,61893,72171,83529,96021,109701,124623,140841,
%U A207165 158409,177381,197811,219753,243261,268389,295191,323721,354033,386181
%N A207165 Number of n X 4 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 1 0 1 vertically.
%C A207165 Column 4 of A207169.
%H A207165 R. H. Hardin, <a href="/A207165/b207165.txt">Table of n, a(n) for n = 1..210</a>
%F A207165 Empirical: a(n) = 9*n^3 + 9*n - 9.
%F A207165 Conjectures from _Colin Barker_, Jun 19 2018: (Start)
%F A207165 G.f.: 9*x*(1 + 5*x - x^2 + x^3) / (1 - x)^4.
%F A207165 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
%F A207165 (End)
%e A207165 Some solutions for n=4:
%e A207165 ..1..1..1..1....1..1..0..0....1..1..0..0....0..0..1..1....1..0..0..1
%e A207165 ..0..1..1..1....0..1..0..0....0..0..1..0....1..0..0..1....0..1..1..0
%e A207165 ..0..1..1..0....0..1..0..0....0..0..1..0....1..0..0..1....0..0..1..0
%e A207165 ..0..0..1..0....0..1..0..0....0..0..1..0....1..0..0..1....0..0..1..0
%Y A207165 Cf. A207169.
%K A207165 nonn
%O A207165 1,1
%A A207165 _R. H. Hardin_, Feb 15 2012