A008796 Molien series for 3-dimensional group [2,3]+ = 223; also for group H_{1,2} of order 384.

1, 0, 2, 1, 4, 2, 7, 4, 10, 7, 14, 10, 19, 14, 24, 19, 30, 24, 37, 30, 44, 37, 52, 44, 61, 52, 70, 61, 80, 70, 91, 80, 102, 91, 114, 102, 127, 114, 140, 127, 154, 140, 169, 154, 184, 169, 200, 184, 217, 200, 234, 217, 252, 234, 271, 252, 290, 271, 310, 290, 331, 310, 352, 331, 374, 352, 397

Offset

0,3

Links

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

E. Bannai, S. T. Dougherty, M. Harada and M. Oura, Type II Codes, Even Unimodular Lattices and Invariant Rings, IEEE Trans. Information Theory, Volume 45, Number 4, 1999, 1194-1205.

Index entries for linear recurrences with constant coefficients, signature (0,2,1,-1,-2,0,1).

Index entries for Molien series

Formula

G.f.: (1+x^4)/((1-x^2)^2*(1-x^3)).

a(n) = (1/72) * (9*(-1)^n*(2*n + 3) + 6*n^2 + 18*n + 29 - 8*A061347[n]). - Ralf Stephan, Apr 28 2014

Maple

seq(coeff(series((1+x^4)/((1-x^2)^2*(1-x^3)), x, n+1), x, n), n = 0..70); # G. C. Greubel, Sep 11 2019

Mathematica

LinearRecurrence[{0, 2, 1, -1, -2, 0, 1}, {1, 0, 2, 1, 4, 2, 7}, 70] (* Harvey P. Dale, Apr 27 2014 *)
CoefficientList[Series[(1+x^4)/((1-x^2)^2*(1-x^3)), {x, 0, 70}], x] (* Vincenzo Librandi, Apr 28 2014 *)

Prog

(PARI) a(n)=(9*(-1)^n*(2*n + 3) + 6*n^2 + 18*n + 24*!(n%3) + 21)/72 \\ Charles R Greathouse IV, Feb 10 2017
(Magma) R<x>:=PowerSeriesRing(Integers(), 70); Coefficients(R!( (1+x^4)/((1-x^2)^2*(1-x^3)) )); // G. C. Greubel, Sep 11 2019
(Sage)
def A008796_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P((1+x^4)/((1-x^2)^2*(1-x^3))).list()
A008796_list(70) # G. C. Greubel, Sep 11 2019
(GAP) a:=[1, 0, 2, 1, 4, 2, 7];; for n in [8..70] do a[n]:=2*a[n-2]+a[n-3]-a[n-4]-2*a[n-5]+a[n-7]; od; a; # G. C. Greubel, Sep 11 2019

Crossrefs

Cf. A008795.

Sequence in context: A256610 A276055 A252866 * A254594 A280948 A325345

Adjacent sequences: A008793 A008794 A008795 * A008797 A008798 A008799

Keyword

nonn,nice,easy

Author

N. J. A. Sloane

Extensions

Definition clarified by N. J. A. Sloane, Feb 02 2018

More terms added by G. C. Greubel, Sep 11 2019

Status

approved