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

1,2

Comments

Column 4 of A224333.

Links

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

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

Example

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

Prog

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

Crossrefs

Cf. A224333.

Sequence in context: A178759 A036397 A247741 * A221352 A271755 A197214

Adjacent sequences: A224326 A224327 A224328 * A224330 A224331 A224332

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