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A207363 Number of n X 3 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 0 1 and 0 1 1 vertically.

%I A207363 #8 Feb 21 2018 07:04:25
%S A207363 6,36,90,225,420,784,1260,2025,2970,4356,6006,8281,10920,14400,18360,
%T A207363 23409,29070,36100,43890,53361,63756,76176,89700,105625,122850,142884,
%U A207363 164430,189225,215760,246016,278256,314721,353430,396900,442890,494209
%N A207363 Number of n X 3 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 0 1 and 0 1 1 vertically.
%C A207363 Column 3 of A207368.
%H A207363 R. H. Hardin, <a href="/A207363/b207363.txt">Table of n, a(n) for n = 1..210</a>
%F A207363 Empirical: a(n) = 2*a(n-1) + 2*a(n-2) - 6*a(n-3) + 6*a(n-5) - 2*a(n-6) - 2*a(n-7) + a(n-8).
%F A207363 Conjectures from _Colin Barker_, Feb 21 2018: (Start)
%F A207363 G.f.: x*(6 + 24*x + 6*x^2 + 9*x^3 + 6*x^4 - 2*x^5 - 2*x^6 + x^7)/ ((1 - x)^5*(1 + x)^3).
%F A207363 a(n) = (n^4 + 6*n^3 + 13*n^2 + 12*n + 4) / 4 for n even.
%F A207363 a(n) = (n^4 + 6*n^3 + 11*n^2 + 6*n) / 4 for n odd.
%F A207363 (End)
%e A207363 Some solutions for n=4:
%e A207363 ..1..1..1....0..0..1....0..1..0....1..1..1....0..1..0....1..1..0....0..1..0
%e A207363 ..1..1..1....0..1..0....1..1..0....1..1..1....1..1..0....0..0..1....0..1..0
%e A207363 ..0..1..0....0..0..1....0..1..0....1..1..1....0..1..0....0..1..0....0..1..0
%e A207363 ..0..1..0....0..1..0....0..1..0....1..1..1....1..0..0....0..0..1....0..1..0
%Y A207363 Cf. A207368.
%K A207363 nonn
%O A207363 1,1
%A A207363 _R. H. Hardin_, Feb 17 2012