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

Author

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

Keywords

• nonn
• easy

Comments

Column 2 of A224333.

Examples

			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
		

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).

Crossrefs

Cf. A224333.

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