A027631 Molien series for Hecke group H_{3,4}.

1, 1, 4, 6, 15, 24, 49, 78, 141, 219, 364, 550, 861, 1261, 1884, 2682, 3856, 5350, 7452, 10100, 13699, 18183, 24104, 31404, 40816, 52297, 66809, 84334, 106110, 132164, 164062, 201896, 247626, 301429, 365727, 440818, 529656, 632693

Offset

0,3

Links

Table of n, a(n) for n=0..37.

Bernhard Runge, On Siegel modular forms, part II, Nagoya Math. J. 138, 179-197 (1995)

Index entries for Molien series

Index entries for linear recurrences with constant coefficients, signature (2, 1, -3, 0, -1, 3, 1, -4, 2, 0, 2, 1, -6, 1, 2, 0, 2, -4, 1, 3, -1, 0, -3, 1, 2, -1).

Formula

G.f.: N_Hecke(x)*(1 + x^2)/((1 - x^2)*(1 - x^4)^3*(1 - x^6)*(1 - x^8)*(1 - x^12)*(1 - x^14)) where N_Hecke(x)= 1 - x^2 + x^4 + 2*x^8 + x^10 + 2*x^12 + x^14 + 5*x^16 + x^18 + 6*x^20 + 2*x^22 + 6*x^24 + 2*x^26 + 6*x^28 + x^30 + 5*x^32 + x^34 + 2*x^36 + x^38 + 2*x^40 + x^44 - x^46 + x^48.

Mathematica

ker = {2, 1, -3, 0, -1, 3, 1, -4, 2, 0, 2, 1}; LinearRecurrence[Join[ker, {-6}, Reverse[ker], {-1}], {1, 1, 4, 6, 15, 24, 49, 78, 141, 219, 364, 550, 861, 1261, 1884, 2682, 3856, 5350, 7452, 10100, 13699, 18183, 24104, 31404, 40816, 52297}, 40] (* Jean-François Alcover, Jun 11 2017 *)

Crossrefs

Sequence in context: A300276 A109731 A369437 * A128620 A358438 A045907

Adjacent sequences: A027628 A027629 A027630 * A027632 A027633 A027634

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Extensions

More terms and formula from Francisco Salinas (franciscodesalinas(AT)hotmail.com), Dec 24 2001

Status

approved