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

1,1

Comments

Column 2 of A224665.

Links

Table of n, a(n) for n=1..23.

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

Example

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

Crossrefs

Sequence in context: A151177 A344419 A002179 * A034541 A180879 A180283

Adjacent sequences: A224656 A224657 A224658 * A224660 A224661 A224662

Keyword

nonn

Author

R. H. Hardin, Apr 14 2013

Status

approved