A224329 Number of idempotent n X n 0..4 matrices of rank n-1.

1, 18, 147, 996, 6245, 37494, 218743, 1249992, 7031241, 39062490, 214843739, 1171874988, 6347656237, 34179687486, 183105468735, 976562499984, 5187988281233, 27465820312482, 144958496093731, 762939453124980

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 4 of A224333.

Examples

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

Links

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

Crossrefs

Cf. A224333.

Programs

PARI

Vec(x*(1 + 6*x - 23*x^2) / ((1 - x)^2*(1 - 5*x)^2) + O(x^40)) \\ Colin Barker, Aug 29 2018

Formula

a(n) = n*(2*5^(n-1)-1).

a(n) = 12*a(n-1) - 46*a(n-2) + 60*a(n-3) - 25*a(n-4).

G.f.: x*(1 + 6*x - 23*x^2) / ((1 - x)^2*(1 - 5*x)^2). - Colin Barker, Aug 29 2018