A029039 - OEIS

A029039

Expansion of 1/((1-x)*(1-x^3)*(1-x^5)*(1-x^6)).

1, 1, 1, 2, 2, 3, 5, 5, 6, 8, 9, 11, 14, 15, 17, 21, 23, 26, 31, 33, 37, 43, 46, 51, 58, 62, 68, 76, 81, 88, 98, 104, 112, 123, 130, 140, 153, 161, 172, 186, 196, 209, 225, 236, 250, 268, 281, 297, 317, 331, 349, 371, 387, 407, 431, 449, 471, 497, 517, 541

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OFFSET

0,4

COMMENTS

Poincaré series [or Poincare series]: 1/((1-x^2)(1-x^6)(1-x^10)(1-x^12)).

Number of partitions of n into parts 1, 3, 5 and 6. - Ilya Gutkovskiy, May 14 2017

REFERENCES

G. van der Geer, Hilbert Modular Surfaces, Springer-Verlag, 1988; p. 192, Note 4.

S. Nagaoka, On the ring of Hilbert modular forms over Z, J. Math. Soc. Japan, 35 (1983) 589-608 + errata.

LINKS

Table of n, a(n) for n=0..59.

Index entries for Molien series

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

FORMULA

a(n) = floor((2*n^3 + 45*n^2 + 282*n + 60*n*[(n mod 3)=0] + 1080)/1080) + [(n mod 30)=6]. - Hoang Xuan Thanh, Jul 02 2025

MATHEMATICA

CoefficientList[Series[1/((1 - x) (1 - x^3) (1 - x^5) (1 - x^6)), {x, 0, 100}], x] (* Vladimir Joseph Stephan Orlovsky, Jun 28 2011 *)

CROSSREFS

Sequence in context: A140200 A289199 A378358 * A316185 A131429 A381057

Adjacent sequences: A029036 A029037 A029038 * A029040 A029041 A029042

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved