A224330 Number of idempotent n X n 0..5 matrices of rank n-1.

1, 22, 213, 1724, 12955, 93306, 653177, 4478968, 30233079, 201553910, 1330255861, 8707129332, 56596340723, 365699432434, 2350924922865, 15045919506416, 95917736853487, 609359740010478, 3859278353399789, 24374389600419820

Offset: 1

Author

R. H. Hardin, formula from M. F. Hasler, William J. Keith and Rob Pratt in the Sequence Fans Mailing List, Apr 03 2013

Keywords

• nonn
• easy

Comments

Column 5 of A224333.

Examples

			Some solutions for n=3:
  0 5 0    1 0 0    1 0 0    0 0 0    0 3 3    0 0 0    1 5 0
  0 1 0    0 1 2    5 0 1    4 1 0    0 1 0    3 1 0    0 0 0
  0 0 1    0 0 0    0 0 1    2 0 1    0 0 1    1 0 1    0 4 1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..210
• Index entries for linear recurrences with constant coefficients, signature (14,-61,84,-36).

Programs

Mathematica

Table[n*(2*6^(n-1)-1),{n, 1, 40}] (* or *)
CoefficientList[Series[(1 + 8*x - 34*x^2) / ((1 - x)^2*(1 - 6*x)^2), {x, 0, 40}], x] (* Stefano Spezia, Aug 29 2018 *)

PARI

Vec(x*(1 + 8*x - 34*x^2) / ((1 - x)^2*(1 - 6*x)^2) + O(x^40)) \\ Colin Barker, Aug 29 2018

Formula

a(n) = n*(2*6^(n-1) - 1).

a(n) = 14*a(n-1) - 61*a(n-2) + 84*a(n-3) - 36*a(n-4).

G.f.: x*(1 + 8*x - 34*x^2) / ((1 - x)^2*(1 - 6*x)^2). - Colin Barker, Aug 29 2018