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%I #12 Jul 24 2017 11:36:46
%S 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,
%T 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,
%U 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
%N Expansion of Jacobi theta constant theta_2^3 /8.
%C Number of ways of writing n as the sum of three odd positive squares.
%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 102.
%H Antti Karttunen, <a href="/A008437/b008437.txt">Table of n, a(n) for n = 0..10000</a>
%H J. E. Jones [Lennard-Jones] and A. E. Ingham, <a href="https://doi.org/10.1098/rspa.1925.0047">On the calculation of certain crystal potential constants and on the cubic crystal of least potential energy</a>, Proc. Royal Soc., A 107 (1925), 636-653 (see p. 650).
%e From _Antti Karttunen_, Jul 24 2017: (Start)
%e a(19) = 3 as 19 = 1+9+9 = 9+1+9 = 9+9+1.
%e a(27) = 4 as 27 = 1+1+25 = 1+25+1 = 25+1+1 = 9+9+9.
%e (End)
%o (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
%Y Equals A085121/8.
%Y Cf. A000004 (the even bisection), A000196, A290081.
%K nonn
%O 0,12
%A _N. J. A. Sloane_.
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