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A008648 Molien series of 3 X 3 upper triangular matrices over GF( 5 ). 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 31 03:48 EDT 2021. Contains 346367 sequences. (Running on oeis4.)