A251285 Number of (n+1) X (1+1) 0..1 arrays with every 2 X 2 subblock having a single 1 or two 1s on the same edge or main diagonally.

9, 22, 52, 125, 297, 710, 1691, 4036, 9621, 22951, 54727, 130529, 311280, 742388, 1770476, 4222417, 10069902, 24015598, 57274225, 136592357, 325756272, 776890181, 1852790060, 4418684023, 10538033895, 25131955837, 59936717455

Offset

1,1

Links

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

Formula

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

Empirical g.f.: x*(9 + 4*x - 10*x^2 + 4*x^3) / (1 - 2*x - 2*x^2 + 3*x^3 - x^4). - Colin Barker, Nov 28 2018

Example

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

Crossrefs

Column 1 of A251292.

Sequence in context: A131895 A323221 A250730 * A197498 A287497 A232024

Adjacent sequences: A251282 A251283 A251284 * A251286 A251287 A251288

Keyword

nonn

Author

R. H. Hardin, Dec 01 2014

Status

approved