|
| |
|
|
A058305
|
|
Numerator of H(n), where H(0)=-1/12, H(n) = number of equivalence classes of positive definite quadratic forms a*x^2+b*x*y+c*y^2 with discriminant b^2-4ac = -n, counting forms equivalent to x^2+y^2 (resp. x^2+x*y+y^2) with multiplicity 1/2 (resp. 1/3).
|
|
1
| |
|
|
-1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 4, 0, 0, 2, 3, 0, 0, 1, 2, 0, 0, 3, 2
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,13
|
|
|
COMMENTS
| a(n) = 0 if n = 1 or 2 (mod 4).
|
|
|
REFERENCES
| D. Zagier, The Eichler-Selberg Trace Formula on SL_2(Z), Appendix to S. Lang, Introduction to Modular Forms, Springer, 1976.
|
|
|
EXAMPLE
| -1/12, 0, 0, 1/3, 1/2, 0, 0, 1, 1, ...
|
|
|
CROSSREFS
| Cf. A058306.
Sequence in context: A123163 A194794 A177893 * A193717 A020808 A198364
Adjacent sequences: A058302 A058303 A058304 * A058306 A058307 A058308
|
|
|
KEYWORD
| sign,frac
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Dec 09 2000
|
| |
|
|
