A259220 Number of (n+1) X (6+1) 0..1 arrays with each 2 X 2 subblock having clockwise pattern 0000 0011 or 0101.

162, 230, 334, 510, 798, 1278, 2078, 3422, 5694, 9566, 16222, 27774, 48030, 83934, 148286, 264926, 478686, 874622, 1615390, 3014238, 5678142, 10789470, 20661854, 39839870, 77278878, 150673118, 295060798, 579951582, 1143447774, 2260270206

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.: 2*x*(81 - 209*x + 31*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*(2^n + 16*Fibonacci(n+3) + 31). - Ehren Metcalfe, Dec 27 2018

Example

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

Crossrefs

Column 6 of A259222.

Sequence in context: A025365 A045227 A066476 * A107120 A045010 A085446

Adjacent sequences: A259217 A259218 A259219 * A259221 A259222 A259223

Keyword

nonn,easy

Author

R. H. Hardin, Jun 21 2015

Status

approved