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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A002266.

Programs

Magma

R:=PowerSeriesRing(Integers(), 70); Coefficients(R!( 1/((1-x)*(1-x^5)*(1-x^25)) )); // G. C. Greubel, Sep 06 2019

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 *)

PARI

my(x='x+O('x^70)); Vec(1/((1-x)*(1-x^5)*(1-x^25))) \\ G. C. Greubel, Sep 06 2019

Sage

def A008648_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P(1/((1-x)*(1-x^5)*(1-x^25))).list()
A008648_list(70) # G. C. Greubel, Sep 06 2019

Formula

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