A224332 Number of idempotent n X n 0..7 matrices of rank n-1.

1, 30, 381, 4092, 40955, 393210, 3670009, 33554424, 301989879, 2684354550, 23622320117, 206158430196, 1786706395123, 15393162788850, 131941395333105, 1125899906842608, 9570149208162287, 81064793292668910, 684547143360315373

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 7 of A224333.

Examples

			Some solutions for n=3:
..1..0..3....0..0..4....0..3..0....0..0..1....1..0..6....0..7..7....1..0..3
..0..1..3....0..1..0....0..1..0....0..1..0....0..1..4....0..1..0....0..1..6
..0..0..0....0..0..1....0..0..1....0..0..1....0..0..0....0..0..1....0..0..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210
• Index entries for linear recurrences with constant coefficients, signature (18,-97,144,-64).

Crossrefs

Cf. A224333.

Programs

Mathematica

Table[n*(2*8^(n-1)-1), {n, 1, 40}] (* Stefano Spezia, Aug 29 2018 *)

PARI

Vec(x*(1 + 12*x - 62*x^2) / ((1 - x)^2*(1 - 8*x)^2) + O(x^40)) \\ Colin Barker, Aug 29 2018

PARI

a(n) = n*(2*8^(n-1)-1); \\ Altug Alkan, Aug 31 2018

Formula

a(n) = n*(2*8^(n-1)-1).

a(n) = 18*a(n-1) - 97*a(n-2) + 144*a(n-3) - 64*a(n-4).

G.f.: x*(1 + 12*x - 62*x^2) / ((1 - x)^2*(1 - 8*x)^2). - Colin Barker, Aug 29 2018