A224327 Number of idempotent n X n 0..2 matrices of rank n-1.

1, 10, 51, 212, 805, 2910, 10199, 34984, 118089, 393650, 1299067, 4251516, 13817453, 44641030, 143489055, 459165008, 1463588497, 4649045850, 14721978563, 46490458660, 146444944821, 460255540910, 1443528741991, 4518872583672

Offset

1,2

Comments

Column 2 of A224333.

Links

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

Index entries for linear recurrences with constant coefficients, signature (8,-22,24,-9).

Formula

a(n) = n*(2*3^(n-1)-1).

a(n) = 8*a(n-1) - 22*a(n-2) + 24*a(n-3) - 9*a(n-4).

G.f.: x*(1 + 2*x - 7*x^2) / ((1 - x)^2*(1 - 3*x)^2). - Colin Barker, Aug 29 2018

Example

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

Crossrefs

Cf. A224333.

Sequence in context: A069038 A213563 A030183 * A219573 A135242 A362673

Adjacent sequences: A224324 A224325 A224326 * A224328 A224329 A224330

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