A008648 Molien series of 3 X 3 upper triangular matrices over GF( 5 ).

1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 9, 9, 9, 9, 9, 11, 11, 11, 11, 11, 13, 13, 13, 13, 13, 15, 15, 15, 15, 15, 18, 18, 18, 18, 18, 21, 21, 21, 21, 21, 24, 24, 24, 24, 24

Offset

0,6

Comments

a(n) is the number of partitions of n into parts 1, 5, and 25. - Joerg Arndt, Sep 07 2019

References

D. J. Benson, Polynomial Invariants of Finite Groups, Cambridge, 1993, p. 105.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 221

Index entries for Molien series

Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, -1, 1).

Formula

G.f.: 1/((1-x)*(1-x^5)*(1-x^25)).

Maple

seq(coeff(series(1/((1-x)*(1-x^5)*(1-x^25)), x, n+1), x, n), n = 0 .. 70); # modified by G. C. Greubel, Sep 06 2019

Mathematica

CoefficientList[Series[1/((1-x)*(1-x^5)*(1-x^25)), {x, 0, 70}], x] (* G. C. Greubel, Sep 06 2019 *)

Prog

(PARI) my(x='x+O('x^70)); Vec(1/((1-x)*(1-x^5)*(1-x^25))) \\ G. C. Greubel, Sep 06 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 70); Coefficients(R!( 1/((1-x)*(1-x^5)*(1-x^25)) )); // G. C. Greubel, Sep 06 2019
(Sage)
def A008648_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P(1/((1-x)*(1-x^5)*(1-x^25))).list()
A008648_list(70) # G. C. Greubel, Sep 06 2019

Crossrefs

Cf. A002266.

Sequence in context: A301506 A002266 A075249 * A154099 A105511 A187183

Adjacent sequences: A008645 A008646 A008647 * A008649 A008650 A008651

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved