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A189154 Number of n X 2 binary arrays without the pattern 0 0 1 1 diagonally, vertically or horizontally 2
4, 16, 64, 225, 784, 2704, 9216, 31329, 106276, 360000, 1218816, 4124961, 13957696, 47224384, 159769600, 540516001, 1828588644, 6186137104, 20927672896, 70798034241, 239508444816, 810252019600, 2741064339456, 9272956793409 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 30 20:17 EST 2021. Contains 349425 sequences. (Running on oeis4.)