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

4, 16, 64, 225, 784, 2704, 9216, 31329, 106276, 360000, 1218816, 4124961, 13957696, 47224384, 159769600, 540516001, 1828588644, 6186137104, 20927672896, 70798034241, 239508444816, 810252019600, 2741064339456, 9272956793409

Offset: 1

Author

R. H. Hardin, Apr 17 2011

Keywords

• nonn

Comments

Column 2 of A189161.

Examples

			Some solutions for 4 X 2:
  1 0   1 0   0 1   1 1   0 1   1 0   1 1   1 1   0 0   1 1
  1 0   1 1   1 0   0 1   1 1   1 1   0 1   1 0   1 1   0 0
  0 1   1 1   1 1   1 0   1 1   1 1   1 1   0 0   1 0   1 1
  1 0   0 0   0 0   0 0   1 0   0 1   0 0   1 1   0 1   0 0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A008937, A189161.

Formula

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

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).

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