A097921 G.f.: (1-x^6)*(1-x^8)/((1-x)*(1-x^2)*(1-x^3)^2*(1-x^4)).

1, 1, 2, 4, 6, 8, 12, 16, 20, 26, 32, 38, 46, 54, 62, 72, 82, 92, 104, 116, 128, 142, 156, 170, 186, 202, 218, 236, 254, 272, 292, 312, 332, 354, 376, 398, 422, 446, 470, 496, 522, 548, 576, 604, 632, 662, 692, 722, 754, 786, 818, 852, 886, 920, 956, 992, 1028, 1066, 1104

Offset

0,3

References

G. van der Geer, Hilbert Modular Surfaces, Springer-Verlag, 1988; p. 188.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for Molien series

Index entries for linear recurrences with constant coefficients, signature (2,-1,1,-2,1).

Formula

a(n) = 2 + floor(n*(n - 1)/3), for n>=2, with a(0)=1, a(1)=1. - G. C. Greubel, Dec 20 2017

Mathematica

CoefficientList[Series[(1 - x^6) (1 - x^8)/((1 - x) (1 - x^2) (1 - x^3)^2 (1 - x^4)), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 29 2014 *)
Join[{1, 1}, LinearRecurrence[{2, -1, 1, -2, 1}, {2, 4, 6, 8, 12}, 30]] (* or *) Join[{1, 1}, Table[2 + Floor[n*(n-1)/3], {n, 2, 30}]] (* G. C. Greubel, Dec 20 2017 *)

Prog

(PARI) a(n)=n*(n-1)\3+2-(n<2) \\ Tani Akinari, Jun 27 2014
(PARI) Vec((1-x^6)*(1-x^8)/((1-x)*(1-x^2)*(1-x^3)^2*(1-x^4)) + O(x^100)) \\ Michel Marcus, Jun 28 2014
(PARI) for(n=0, 30, print1(if(n==0, 1, if(n==1, 1, 2 + floor(n*(n-1)/3))), ", ")) \\ G. C. Greubel, Dec 20 2017
(Magma) [1, 1] cat [2 + Floor(n*(n-1)/3): n in [2..30]]; // G. C. Greubel, Dec 20 2017

Crossrefs

Sequence in context: A333255 A346729 A346311 * A185976 A117146 A061553

Adjacent sequences: A097918 A097919 A097920 * A097922 A097923 A097924

Keyword

nonn

Author

N. J. A. Sloane, Sep 05 2004

Status

approved