cp's OEIS Frontend

A189154 Number of n X 2 binary arrays without the pattern 0 0 1 1 diagonally, vertically or horizontally.

%I A189154 #17 Jul 22 2025 11:34:43
%S A189154 4,16,64,225,784,2704,9216,31329,106276,360000,1218816,4124961,
%T A189154 13957696,47224384,159769600,540516001,1828588644,6186137104,
%U A189154 20927672896,70798034241,239508444816,810252019600,2741064339456,9272956793409
%N A189154 Number of n X 2 binary arrays without the pattern 0 0 1 1 diagonally, vertically or horizontally.
%C A189154 Column 2 of A189161.
%H A189154 R. H. Hardin, <a href="/A189154/b189154.txt">Table of n, a(n) for n = 1..200</a>
%F A189154 a(n) = A008937(n+1)^2.
%F A189154 Empirical: a(n) = 4*a(n-1) - a(n-2) - 14*a(n-4) + 4*a(n-5) + 2*a(n-6) + 8*a(n-7) - a(n-8) - a(n-10).
%F A189154 Empirical g.f.: x*(4 + 4*x^2 - 15*x^3 + 4*x^4 + x^5 + 8*x^6 - x^7 - x^9) / ((1 - x)*(1 + x + x^2 - x^3)*(1 - x - x^2 - x^3)*(1 - 3*x - x^2 - x^3)). - _Colin Barker_, Feb 28 2018
%e A189154 Some solutions for 4 X 2:
%e A189154   1 0   1 0   0 1   1 1   0 1   1 0   1 1   1 1   0 0   1 1
%e A189154   1 0   1 1   1 0   0 1   1 1   1 1   0 1   1 0   1 1   0 0
%e A189154   0 1   1 1   1 1   1 0   1 1   1 1   1 1   0 0   1 0   1 1
%e A189154   1 0   0 0   0 0   0 0   1 0   0 1   0 0   1 1   0 1   0 0
%Y A189154 Cf. A008937, A189161.
%K A189154 nonn
%O A189154 1,1
%A A189154 _R. H. Hardin_, Apr 17 2011