A224338 Number of idempotent 7 X 7 0..n matrices of rank 6.

889, 10199, 57337, 218743, 653177, 1647079, 3670009, 7440167, 13999993, 24801847, 41803769, 67575319, 105413497, 159468743, 234881017, 337925959, 476171129, 658642327, 895999993, 1200725687, 1587318649, 2072502439, 2675441657

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 7 of A224333.

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

Cf. A224333.

Programs

PARI

Vec(-7*x*(x^6-8*x^5+29*x^4+64*x^3+659*x^2+568*x+127)/(x-1)^7 + O(x^100)) \\ Colin Barker, Sep 20 2014

Formula

a(n) = 14*n^6 + 84*n^5 + 210*n^4 + 280*n^3 + 210*n^2 + 84*n + 7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7). - Colin Barker, Sep 20 2014

G.f.: -7*x*(x^6-8*x^5+29*x^4+64*x^3+659*x^2+568*x+127) / (x-1)^7. - Colin Barker, Sep 20 2014