A051629 Poincaré series [or Poincare series] for Gamma_2(1,2).

1, 0, 0, 0, 2, 0, 2, 0, 4, 0, 5, 0, 9, 0, 9, 0, 15, 0, 17, 1, 23, 1, 27, 3, 36, 3, 39, 6, 51, 7, 57, 11, 69, 13, 78, 19, 94, 21, 102, 29, 122, 33, 134, 42, 154, 48, 170, 60, 195, 66, 210, 81, 240, 90, 260, 106, 290, 118, 315, 138, 351, 150, 375, 174, 417

Offset

0,5

Links

Table of n, a(n) for n=0..64.

Takeyoshi Kogiso and Koji Tsushima, On an algebra of Siegel modular forms associated with the theta group Gamma_2(1,2), Tsukuba J. Math. 22 (1998), 645-656.

B. Runge, Codes and Siegel modular forms, Discrete Math. 148 (1996), 175-204, p. 203, first displayed formula.

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

Maple

(1+x^6+x^8+x^10+x^19+x^21+x^23+x^29)/((1-x^4)^2*(1-x^6)*(1-x^12));

Mathematica

Join[{1, 0, 0, 0}, LinearRecurrence[{1, 0, 0, 1, -1, 1, -1, 0, 0, -1, 1, 1, -1, 0, 0, -1, 1, -1, 1, 0, 0, 1, -1}, {2, 0, 2, 0, 4, 0, 5, 0, 9, 0, 9, 0, 15, 0, 17, 1, 23, 1, 27, 3, 36, 3, 39}, 61]] (* Jean-François Alcover, Jul 31 2019 *)

Crossrefs

Sequence in context: A029187 A201863 A035385 * A052120 A179461 A364568

Adjacent sequences: A051626 A051627 A051628 * A051630 A051631 A051632

Keyword

nonn,nice,easy

Author

N. J. A. Sloane

Status

approved