A224334 Number of idempotent 3 X 3 0..n matrices of rank 2.

21, 51, 93, 147, 213, 291, 381, 483, 597, 723, 861, 1011, 1173, 1347, 1533, 1731, 1941, 2163, 2397, 2643, 2901, 3171, 3453, 3747, 4053, 4371, 4701, 5043, 5397, 5763, 6141, 6531, 6933, 7347, 7773, 8211, 8661, 9123, 9597, 10083, 10581, 11091, 11613, 12147

Offset

1,1

Comments

Row 3 of A224333.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(n) = 6*n^2 + 12*n + 3.

From Colin Barker, Feb 23 2018: (Start)

G.f.: 3*x*(7 - 4*x + x^2) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>3.

(End)

Example

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

Prog

(PARI) a(n) = 6*n^2 + 12*n + 3 \\ Charles R Greathouse IV, Jun 17 2017
(PARI) Vec(3*x*(7 - 4*x + x^2) / (1 - x)^3 + O(x^60)) \\ Colin Barker, Feb 23 2018

Crossrefs

Cf. A224333.

Sequence in context: A235884 A053178 A166150 * A305002 A242236 A235877

Adjacent sequences: A224331 A224332 A224333 * A224335 A224336 A224337

Keyword

nonn,easy

Author

R. H. Hardin, formula via M. F. Hasler William J. Keith and Rob Pratt in the Sequence Fans Mailing List, Apr 03 2013

Status

approved