A097535 Dimensions of spaces of cusp forms.

1, 1, 1, 2, 2, 3, 4, 4, 4, 5, 5, 5, 6, 7, 7, 8, 8, 8, 9, 9, 9, 12, 12, 12, 13, 13, 13, 14, 14, 15, 16, 16, 16, 17, 17, 17, 18, 19, 19, 20, 20, 20, 21, 21, 21, 24, 24, 24, 25, 25, 25, 26, 26, 27, 28, 28, 28, 29, 29, 29, 30, 31, 31, 32, 32, 32, 33, 33, 33, 36, 36, 36, 37, 37, 37, 38, 38, 39, 40, 40, 40, 41, 41, 41, 42, 43, 43, 44, 44, 44, 45, 45, 45, 48, 48, 48, 49

Offset

4,4

References

H. Petersson, Modulfunktionen und Quadratische Formen, Springer-Verlag, 1982; p. 186.

Links

Table of n, a(n) for n=4..100.

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

Formula

a(n+24m) = a(n) + 12m for m >= 1.

a(n)= +a(n-1) +a(n-24) -a(n-25). - R. J. Mathar, Oct 01 2011

G.f.: x^4*(1 + x^3 + x^5 + x^6 + x^9 + x^12 + x^13 + x^15 + x^18 + 3*x^21) / ((1 - x)^2*(1 + x)*(1 - x + x^2)*(1 + x^2)*(1 + x + x^2)*(1 - x^2 + x^4)*(1 + x^4)*(1 - x^4 + x^8)). - Colin Barker, Jun 06 2019

Mathematica

LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1}, {1, 1, 1, 2, 2, 3, 4, 4, 4, 5, 5, 5, 6, 7, 7, 8, 8, 8, 9, 9, 9, 12, 12, 12, 13}, 120] (* Harvey P. Dale, May 11 2016 *)

Prog

(PARI) Vec(x^4*(1 + x^3 + x^5 + x^6 + x^9 + x^12 + x^13 + x^15 + x^18 + 3*x^21) / ((1 - x)^2*(1 + x)*(1 - x + x^2)*(1 + x^2)*(1 + x + x^2)*(1 - x^2 + x^4)*(1 + x^4)*(1 - x^4 + x^8)) + O(x^40)) \\ Colin Barker, Jun 06 2019

Crossrefs

Sequence in context: A034136 A362918 A189638 * A060018 A089576 A076642

Adjacent sequences: A097532 A097533 A097534 * A097536 A097537 A097538

Keyword

nonn,easy

Author

N. J. A. Sloane, Aug 27 2004

Status

approved