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

Author

R. H. Hardin, Apr 10 2013

Keywords

• nonn

Comments

Column 2 of A224550.

Examples

			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
		

Links

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

Crossrefs

Cf. A224550.

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