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

1,1

Comments

Column 2 of A189161.

Links

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

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

Example

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

Crossrefs

Cf. A008937, A189161.

Sequence in context: A343200 A227312 A267729 * A189336 A262334 A065738

Adjacent sequences: A189151 A189152 A189153 * A189155 A189156 A189157

Keyword

nonn

Author

R. H. Hardin, Apr 17 2011

Status

approved