A259218 Number of (n+1) X (4+1) 0..1 arrays with each 2 X 2 subblock having clockwise pattern 0000 0011 or 0101.

45, 71, 112, 183, 303, 510, 869, 1499, 2616, 4619, 8251, 14910, 27249, 50343, 93968, 177071, 336567, 644702, 1243405, 2412387, 4704360, 9213891, 18112547, 35715038, 70604793, 139874255, 277587904, 551679879, 1097703231, 2186254014, 4357699061

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*(45 - 109*x + 8*x^2 + 64*x^3) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)). - Colin Barker, Dec 24 2018

a(n) = 2^(n+1)+8+11*A000045(n+3). - R. J. Mathar, Oct 09 2020

Example

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

Crossrefs

Column 4 of A259222.

Sequence in context: A026043 A330850 A053720 * A093764 A194426 A082452

Adjacent sequences: A259215 A259216 A259217 * A259219 A259220 A259221

Keyword

nonn,easy

Author

R. H. Hardin, Jun 21 2015

Status

approved