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A207118 Number of n X 3 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 0 1 and 0 1 1 vertically.

%I A207118 #8 Feb 20 2018 12:12:16
%S A207118 6,36,102,289,612,1296,2340,4225,6890,11236,17066,25921,37352,53824,
%T A207118 74472,103041,138030,184900,241230,314721,401676,512656,642252,804609,
%U A207118 992082,1223236,1487570,1809025,2173520,2611456,3104336,3690241,4345302
%N A207118 Number of n X 3 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 0 1 and 0 1 1 vertically.
%C A207118 Column 3 of A207123.
%H A207118 R. H. Hardin, <a href="/A207118/b207118.txt">Table of n, a(n) for n = 1..210</a>
%F A207118 Empirical: a(n) = 2*a(n-1) +4*a(n-2) -10*a(n-3) -5*a(n-4) +20*a(n-5) -20*a(n-7) +5*a(n-8) +10*a(n-9) -4*a(n-10) -2*a(n-11) +a(n-12).
%F A207118 Conjectures from _Colin Barker_, Feb 20 2018: (Start)
%F A207118 G.f.: x*(6 + 24*x + 6*x^2 + x^3 + 16*x^4 - 4*x^5 - 20*x^6 + 6*x^7 + 10*x^8 - 4*x^9 - 2*x^10 + x^11) / ((1 - x)^7*(1 + x)^5).
%F A207118 a(n) = (n^6 + 24*n^5 + 208*n^4 + 816*n^3 + 1600*n^2 + 1536*n + 576) / 576 for n even.
%F A207118 a(n) = (n^6 + 24*n^5 + 205*n^4 + 768*n^3 + 1315*n^2 + 936*n + 207) / 576 for n odd.
%F A207118 (End)
%e A207118 Some solutions for n=4:
%e A207118 ..1..1..0....1..0..1....1..1..0....1..1..1....0..0..0....0..1..1....1..1..1
%e A207118 ..0..0..0....0..1..1....1..1..0....1..1..1....0..1..1....0..1..1....1..1..1
%e A207118 ..0..0..0....0..0..0....1..1..0....1..1..1....0..0..0....0..1..1....0..1..1
%e A207118 ..0..0..0....0..0..0....1..1..0....1..1..1....0..0..0....0..1..1....0..1..1
%Y A207118 Cf. A207123.
%K A207118 nonn
%O A207118 1,1
%A A207118 _R. H. Hardin_, Feb 15 2012