A224525 Number of idempotent 3 X 3 0..n matrices of rank 1.

27, 69, 123, 195, 273, 375, 477, 603, 735, 885, 1035, 1221, 1395, 1593, 1803, 2031, 2253, 2511, 2757, 3039, 3321, 3615, 3909, 4251, 4575, 4917, 5271, 5649, 6015, 6429, 6819, 7245, 7671, 8109, 8559, 9051, 9513, 9999, 10497, 11031, 11541, 12099, 12633

Offset: 1

Author

R. H. Hardin, Apr 09 2013

Keywords

• nonn

Comments

Row 3 of A224524.

Examples

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

Links

• Robert Israel, Table of n, a(n) for n = 1..10000 (first 80 terms from R. H. Hardin)

Crossrefs

Cf. A002541, A224524.

Programs

Maple

f:= k -> 6*k^2 + 18*k + 3 + 6 * add(floor(k/m),m=2..k):
map(f, [$1..50]); # Robert Israel, Dec 15 2019

Formula

a(n) = 6*n^2 + 18*n + 3 + 6 * A002541(n). - Robert Israel, Dec 15 2019