A224331 Number of idempotent n X n 0..6 matrices of rank n-1.

1, 26, 291, 2740, 24005, 201678, 1647079, 13176680, 103766409, 807072130, 6214455467, 47455841820, 359873467213, 2712892291382, 20346692185455, 151921968318160, 1129919639366417, 8374698503539434, 61879716720597043

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 6 of A224333.

Examples

			Some solutions for n=3:
..1..5..0....0..3..6....1..0..0....0..0..0....1..0..0....1..0..0....0..0..0
..0..0..0....0..1..0....0..1..0....6..1..0....0..1..0....0..1..0....2..1..0
..0..2..1....0..0..1....0..0..0....4..0..1....1..6..0....3..4..0....3..0..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210
• Index entries for linear recurrences with constant coefficients, signature (16,-78,112,-49).

Crossrefs

Cf. A224333.

Programs

Mathematica

Table[n*(2*7^(n-1)-1), {n, 1, 40}] (* or *)
CoefficientList[Series[(1 + 10*x - 47*x^2) / ((1 - x)^2*(1 - 7*x)^2) , {x, 0, 40}], x] (* Stefano Spezia, Aug 29 2018 *)

PARI

Vec(x*(1 + 10*x - 47*x^2) / ((1 - x)^2*(1 - 7*x)^2) + O(x^40)) \\ Colin Barker, Aug 29 2018

Formula

a(n) = n*(2*7^(n-1)-1).

a(n) = 16*a(n-1) - 78*a(n-2) + 112*a(n-3) - 49*a(n-4).

G.f.: x*(1 + 10*x - 47*x^2) / ((1 - x)^2*(1 - 7*x)^2). - Colin Barker, Aug 29 2018