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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
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
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
KEYWORD
nonn,easy
STATUS
approved