A224659 Number of n X n 0..2 matrices with each 2 X 2 subblock idempotent.

3, 12, 50, 108, 260, 542, 1126, 2230, 4336, 8246, 15458, 28608, 52420, 95240, 171814, 308056, 549384, 975130, 1723482, 3034498, 5324180, 9311762, 16238070

Offset: 1

Author

R. H. Hardin, Apr 14 2013

Keywords

• nonn

Comments

Column 2 of A224665.

Examples

			Some solutions for n=3:
..1..0..0....1..0..0....1..1..2....1..0..1....1..0..2....1..0..0....1..1..1
..0..0..0....1..0..1....0..0..0....1..0..1....0..0..1....0..0..0....0..0..0
..2..1..1....2..0..1....0..1..1....0..0..1....0..0..1....0..1..1....1..1..1
		

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) for n>10.

Empirical g.f.: x*(3 - 6*x + 14*x^2 - 63*x^3 + 116*x^4 - 80*x^5 + 7*x^6 + 12*x^8 + 3*x^9) / ((1 - x)^3*(1 - x - x^2)^3). - Colin Barker, Feb 17 2018