A224543 Number of (n+1) X (n+1) 0..1 matrices with each 2 X 2 subblock idempotent.

8, 32, 78, 196, 428, 916, 1858, 3678, 7096, 13458, 25150, 46466, 85028, 154356, 278298, 498792, 889320, 1578248, 2789166, 4910498, 8615348, 15067462, 26274538, 45693286

Offset: 1

Author

R. H. Hardin, Apr 10 2013

Keywords

• nonn

Comments

Diagonal of A224550.

Examples

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

Crossrefs

Cf. A224550.

Formula

Empirical: a(n) = 6*a(n-1) - 12*a(n-2) + 5*a(n-3) + 12*a(n-4) - 12*a(n-5) - 3*a(n-6) + 6*a(n-7) - a(n-9).

Empirical g.f.: 2*x*(4 - 8*x - 9*x^2 + 36*x^3 - 34*x^4 + 11*x^5 - 5*x^6 + 7*x^7 + x^8) / ((1 - x)^3*(1 - x - x^2)^3). - Colin Barker, Aug 30 2018