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

1,2

Comments

Column 5 of A224333.

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).

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

Example

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

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 *)

Prog

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

Crossrefs

Sequence in context: A125385 A126543 A232019 * A223928 A224052 A224305

Adjacent sequences: A224327 A224328 A224329 * A224331 A224332 A224333

Keyword

nonn,easy

Author

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

Status

approved