A224336 Number of idempotent 5 X 5 0..n matrices of rank 4.

155, 805, 2555, 6245, 12955, 24005, 40955, 65605, 99995, 146405, 207355, 285605, 384155, 506245, 655355, 835205, 1049755, 1303205, 1599995, 1944805, 2342555, 2798405, 3317755, 3906245, 4569755, 5314405, 6146555, 7072805, 8099995, 9235205, 10485755, 11859205, 13363355

Offset

1,1

Links

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

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

a(n) = 10*n^4 + 40*n^3 + 60*n^2 + 40*n + 5.

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). - Colin Barker, Sep 20 2014

G.f.: -5*x*(x^4-6*x^3+16*x^2+6*x+31) / (x-1)^5. - Colin Barker, Sep 20 2014

E.g.f.: 5*(exp(x)*(1 + 30*x + 50*x^2 + 20*x^3 + 2*x^4) - 1). - Stefano Spezia, Aug 25 2025

Example

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

Prog

(PARI) Vec(-5*x*(x^4-6*x^3+16*x^2+6*x+31)/(x-1)^5 + O(x^100)) \\ Colin Barker, Sep 20 2014

Crossrefs

Row 5 of A224333.

Sequence in context: A129640 A028382 A250936 * A218328 A101535 A010086

Adjacent sequences: A224333 A224334 A224335 * A224337 A224338 A224339

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