A008437 Expansion of Jacobi theta constant theta_2^3 /8.

0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0

Offset

0,12

Comments

Number of ways of writing n as the sum of three odd positive squares.

References

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 102.

Links

Antti Karttunen, Table of n, a(n) for n = 0..10000

J. E. Jones [Lennard-Jones] and A. E. Ingham, On the calculation of certain crystal potential constants and on the cubic crystal of least potential energy, Proc. Royal Soc., A 107 (1925), 636-653 (see p. 650).

Example

From Antti Karttunen, Jul 24 2017: (Start)
a(19) = 3 as 19 = 1+9+9 = 9+1+9 = 9+9+1.
a(27) = 4 as 27 = 1+1+25 = 1+25+1 = 25+1+1 = 9+9+9.
(End)

Prog

(Scheme) (define (A008437 n) (cond ((< n 3) 0) ((even? n) 0) (else (let loop ((k (- (A000196 n) (modulo (+ 1 (A000196 n)) 2))) (s 0)) (if (< k 1) s (loop (- k 2) (+ s (A290081 (- n (* k k)))))))))) ;; Antti Karttunen, Jul 24 2017

Crossrefs

Equals A085121/8.

Cf. A000004 (the even bisection), A000196, A290081.

Sequence in context: A308229 A318673 A151795 * A366076 A324326 A341743

Adjacent sequences: A008434 A008435 A008436 * A008438 A008439 A008440

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved