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

1,1

Comments

Row 3 of A224524.

Links

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

Formula

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

Example

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

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

Crossrefs

Cf. A002541, A224524.

Sequence in context: A065008 A250134 A116353 * A219130 A116302 A181976

Adjacent sequences: A224522 A224523 A224524 * A224526 A224527 A224528

Keyword

nonn

Author

R. H. Hardin, Apr 09 2013

Status

approved