A097923 Expansion of (1+x^20)/((1-x)*(1-x^3)*(1-x^5)).

1, 1, 1, 2, 2, 3, 4, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 17, 18, 21, 23, 24, 27, 29, 32, 35, 37, 40, 43, 47, 50, 53, 57, 60, 65, 69, 72, 77, 81, 86, 91, 95, 100, 105, 111, 116, 121, 127, 132, 139, 145, 150, 157, 163, 170, 177, 183, 190, 197, 205, 212, 219, 227, 234, 243, 251, 258

Offset

0,4

References

G. van der Geer, Hilbert Modular Surfaces, Springer-Verlag, 1988; p. 191, Cor. 2.2.

Links

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

G. van der Geer, Hilbert Modular Surfaces, in: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, Band 16, Springer-Verlag (1988).

Index entries for Molien series

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

Formula

G.f.: (1+x^20)/((1-x)*(1-x^3)*(1-x^5)).

Mathematica

CoefficientList[Series[(1 + x^20)/((1 - x)*(1 - x^3)*(1 - x^5)), {x, 0, 100}], x] (* Wesley Ivan Hurt, Mar 30 2017 *)
LinearRecurrence[{1, 0, 1, -1, 1, -1, 0, -1, 1}, {1, 1, 1, 2, 2, 3, 4, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 17, 18, 21}, 68] (* G. C. Greubel, Dec 20 2017; more initial terms by Georg Fischer, Apr 08 2019 *)

Prog

(PARI) x='x+O('x^30); Vec((1+x^20)/((1-x)*(1-x^3)*(1-x^5))) \\ G. C. Greubel, Dec 20 2017
(Magma) I:=[1, 1, 1, 2, 2, 3, 4, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 17, 18, 21];
[n le 21 select I[n] else Self(n-1) + Self(n-3) - Self(n-4) + Self(n-5) - Self(n-6) - Self(n-8) + Self(n-9): n in [1..80]]; // G. C. Greubel, Dec 20 2017; more initial terms by Georg Fischer, Apr 03 2019

Crossrefs

Sequence in context: A011885 A211524 A008672 * A027582 A259198 A011880

Adjacent sequences: A097920 A097921 A097922 * A097924 A097925 A097926

Keyword

nonn,easy

Author

N. J. A. Sloane, Sep 05 2004

Status

approved