A259290 Number of (n+1) X (1+1) 0..1 arrays with each 2 X 2 subblock having clockwise pattern 0001 0101 or 0111.

10, 26, 66, 170, 434, 1114, 2850, 7306, 18706, 47930, 122754, 314474, 805490, 2063386, 5285346, 13538890, 34680274, 88835834, 227556930, 582900266, 1493127986, 3824729050, 9797240994, 25096157194, 64285121170, 164669749946

Offset

1,1

Links

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

Formula

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

Conjectures from Colin Barker, Dec 25 2018: (Start)

G.f.: 2*x*(5 + 8*x) / (1 - x - 4*x^2).

a(n) = (2^(1-n)*((1-sqrt(17))^n*(-4+sqrt(17)) + (1+sqrt(17))^n*(4+sqrt(17)))) / sqrt(17).

(End)

Example

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

Crossrefs

Column 1 of A259297.

Sequence in context: A332596 A134420 A144255 * A072379 A005970 A192254

Adjacent sequences: A259287 A259288 A259289 * A259291 A259292 A259293

Keyword

nonn

Author

R. H. Hardin, Jun 23 2015

Status

approved