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

%I

%S 4,16,64,225,784,2704,9216,31329,106276,360000,1218816,4124961,

%T 13957696,47224384,159769600,540516001,1828588644,6186137104,

%U 20927672896,70798034241,239508444816,810252019600,2741064339456,9272956793409

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

%C Column 2 of A189161.

%H R. H. Hardin, <a href="/A189154/b189154.txt">Table of n, a(n) for n = 1..200</a>

%F a(n) = A008937(n+1)^2.

%F 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 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 Some solutions for 4 X 2:

%e 1 0 1 0 0 1 1 1 0 1 1 0 1 1 1 1 0 0 1 1

%e 1 0 1 1 1 0 0 1 1 1 1 1 0 1 1 0 1 1 0 0

%e 0 1 1 1 1 1 1 0 1 1 1 1 1 1 0 0 1 0 1 1

%e 1 0 0 0 0 0 0 0 1 0 0 1 0 0 1 1 0 1 0 0

%Y Cf. A008937, A189161.

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 17 2011

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Last modified January 23 03:15 EST 2022. Contains 350504 sequences. (Running on oeis4.)