A224544 Number of (n+1) X 3 0..1 matrices with each 2 X 2 subblock idempotent.

16, 32, 52, 86, 137, 218, 345, 547, 869, 1385, 2214, 3549, 5702, 9178, 14794, 23872, 38551, 62292, 100695, 162821, 263331, 425947, 689052, 1114751, 1803532, 2917988, 4721200, 7638842, 12359669, 19998110, 32357349, 52354999, 84711857, 137066333

Offset

1,1

Comments

Column 2 of A224550.

Links

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

Formula

Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + a(n-3) + 2*a(n-4) - a(n-5).

Empirical g.f.: x*(16 - 32*x + 4*x^2 + 22*x^3 - 11*x^4) / ((1 - x)^3*(1 - x - x^2)). - Colin Barker, Aug 30 2018

Example

Some solutions for n=3:
..1..1..1....0..0..0....1..1..1....1..0..0....1..0..0....1..0..0....1..0..0
..0..0..0....0..0..0....0..0..0....1..0..0....1..0..0....0..0..0....1..0..1
..0..0..0....0..0..0....0..0..1....1..0..0....1..0..0....0..0..0....1..0..1
..0..0..0....0..1..1....0..0..1....1..0..0....0..0..0....1..1..1....1..0..1

Crossrefs

Cf. A224550.

Sequence in context: A082294 A048946 A260050 * A255994 A204645 A236323

Adjacent sequences: A224541 A224542 A224543 * A224545 A224546 A224547

Keyword

nonn

Author

R. H. Hardin, Apr 10 2013

Status

approved