A259219 Number of (n+1) X (5+1) 0..1 arrays with each 2 X 2 subblock having clockwise pattern 0000 0011 or 0101.

85, 127, 192, 303, 487, 798, 1325, 2227, 3784, 6499, 11283, 19806, 35161, 63135, 114656, 210535, 390703, 732286, 1385109, 2641659, 5075320, 9814107, 19083707, 37286398, 73147297, 143988103, 284244240, 562450047, 1115129719, 2214450654

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Index entries for linear recurrences with constant coefficients, signature (4,-4,-1,2).

Formula

a(n) = 4*a(n-1) - 4*a(n-2) - a(n-3) + 2*a(n-4).

G.f.: x*(85 - 213*x + 24*x^2 + 128*x^3) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)). - Colin Barker, Dec 24 2018

From the above formulae, a(n) = 2^(n+1) + 19*Fibonacci(n+3) + 24. - Ehren Metcalfe, Dec 27 2018

Example

Some solutions for n=4:
  0 1 0 1 0 1    1 1 1 1 1 1    1 0 0 0 0 0    0 0 0 1 1 1
  0 1 0 1 0 1    0 0 0 0 0 0    0 1 1 1 1 1    1 1 1 0 0 0
  0 1 0 1 0 1    1 1 1 1 1 1    1 0 0 0 0 0    0 0 0 1 1 1
  0 1 0 1 0 1    0 0 0 0 0 0    0 1 1 1 1 1    1 1 1 0 0 0
  1 0 1 0 1 0    1 1 1 1 1 1    1 0 0 0 0 0    0 0 0 1 1 1

Crossrefs

Column 5 of A259222.

Sequence in context: A066474 A161479 A027453 * A273123 A239527 A029471

Adjacent sequences: A259216 A259217 A259218 * A259220 A259221 A259222

Keyword

nonn,easy

Author

R. H. Hardin, Jun 21 2015

Status

approved