A259221 Number of (n+1) X (7+1) 0..1 arrays with each 2 X 2 subblock having clockwise pattern 0000 0011 or 0101.

311, 421, 588, 869, 1325, 2078, 3319, 5377, 8804, 14545, 24225, 40670, 68843, 117557, 202636, 352813, 620837, 1104574, 1987407, 3616121, 6651956, 12365081, 23211193, 43964734, 83952995, 161472013, 312533724, 608223317, 1189192349, 2334286430

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*(311 - 823*x + 148*x^2 + 512*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) + 53*Fibonacci(n+3) + 148. - Ehren Metcalfe, Dec 27 2018

Example

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

Crossrefs

Column 7 of A259222.

Sequence in context: A059225 A157717 A113155 * A142626 A142950 A323050

Adjacent sequences: A259218 A259219 A259220 * A259222 A259223 A259224

Keyword

nonn,easy

Author

R. H. Hardin, Jun 21 2015

Status

approved