A224337 Number of idempotent 6X6 0..n matrices of rank 5.

378, 2910, 12282, 37494, 93306, 201678, 393210, 708582, 1199994, 1932606, 2985978, 4455510, 6453882, 9112494, 12582906, 17038278, 22674810, 29713182, 38399994, 49009206, 61843578, 77236110, 95551482, 117187494, 142576506, 172186878

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

Row 6 of A224333.

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Programs

PARI

Vec(-6*x*(x^5-7*x^4+18*x^3-82*x^2-107*x-63)/(x-1)^6 + O(x^100)) \\ Colin Barker, Sep 20 2014

Formula

a(n) = 12*n^5 + 60*n^4 + 120*n^3 + 120*n^2 + 60*n + 6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6). - Colin Barker, Sep 20 2014

G.f.: -6*x*(x^5-7*x^4+18*x^3-82*x^2-107*x-63) / (x-1)^6. - Colin Barker, Sep 20 2014