cp's OEIS Frontend

A206982 Number of n X 3 0..1 arrays avoiding the patterns 0 1 0 or 1 0 1 in any row, column, diagonal or antidiagonal.

%I A206982 #11 Jun 17 2018 14:40:04
%S A206982 6,36,58,158,420,1066,2754,7140,18430,47602,123028,317870,821262,
%T A206982 2121988,5482746,14166078,36601876,94570810,244348930,631340852,
%U A206982 1631238222,4214740594,10889910564,28136999454,72699470734,187838545012
%N A206982 Number of n X 3 0..1 arrays avoiding the patterns 0 1 0 or 1 0 1 in any row, column, diagonal or antidiagonal.
%C A206982 Column 3 of A206987.
%H A206982 R. H. Hardin, <a href="/A206982/b206982.txt">Table of n, a(n) for n = 1..210</a>
%F A206982 Empirical: a(n) = 2*a(n-1) + a(n-2) + 2*a(n-3) - a(n-4) - 2*a(n-5) for n>7.
%F A206982 Empirical g.f.: 2*x*(1 - x)*(3 + 15*x + 5*x^2 + 2*x^3 - 8*x^4 - 8*x^5) / (1 - 2*x - x^2 - 2*x^3 + x^4 + 2*x^5). - _Colin Barker_, Jun 17 2018
%e A206982 Some solutions for n=4:
%e A206982   1 0 0    0 0 0    1 0 0    0 0 1    0 1 1    0 1 1    1 1 0
%e A206982   1 1 1    1 0 0    1 0 0    1 1 1    0 0 0    0 0 1    0 0 0
%e A206982   1 1 1    1 0 0    1 1 0    1 1 1    0 0 0    0 0 0    0 0 0
%e A206982   1 0 0    0 0 0    1 1 0    0 0 0    1 1 0    0 0 0    0 0 1
%Y A206982 Cf. A206987.
%K A206982 nonn
%O A206982 1,1
%A A206982 _R. H. Hardin_, Feb 14 2012