|
Search: id:A098108
|
|
|
| A098108 |
|
1 if n is an odd square otherwise 0. |
|
+0
2
|
|
| 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
(list; graph; listen)
|
|
|
OFFSET
|
0,1
|
|
|
COMMENT
|
Motivated by expansion of Jacobi theta function theta_2(x) = Sum_{m = -infinity..infinity} x^((m+1/2)^2) = 2 Sum_{m odd > 0} q^(m^2/4).
Multiplicative with a(p^e) = 1 if 2 divides e and p > 2, 0 otherwise. Mitch Harris (Harris.Mitchell(AT)mgh.harvard.edu) Jun 09, 2005.
|
|
REFERENCES
|
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 104, [5n].
J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 102.
N. J. Fine, Basic Hypergeometric Series and Applications, Amer. Math. Soc., 1988; p. 93, Eq. (34.12).
E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, Cambridge Univ. Press, 4th ed., 1963, p. 464.
|
|
LINKS
|
Index entries for characteristic functions
Eric Weisstein's World of Mathematics, Jacobi Theta Functions
|
|
MAPLE
|
add(x^((m+1/2)^2), m=-10..10);
|
|
CROSSREFS
|
Cf. A000122 (theta_3), A002448 (theta_4).
Sequence in context: A130638 A030217 A030215 this_sequence A030214 A025464 A162518
Adjacent sequences: A098105 A098106 A098107 this_sequence A098109 A098110 A098111
|
|
KEYWORD
|
nonn,mult
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com), Nov 03 2004
|
|
|
Search completed in 0.002 seconds
|
