This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A008437 #14 Jul 08 2025 01:04:03 %S A008437 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 A008437 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 A008437 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 A008437 Expansion of Jacobi theta constant theta_2^3 /8. %C A008437 Number of ways of writing n as the sum of three odd positive squares. %D A008437 J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 102. %H A008437 Antti Karttunen, <a href="/A008437/b008437.txt">Table of n, a(n) for n = 0..10000</a> %H A008437 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 A008437 From _Antti Karttunen_, Jul 24 2017: (Start) %e A008437 a(19) = 3 as 19 = 1+9+9 = 9+1+9 = 9+9+1. %e A008437 a(27) = 4 as 27 = 1+1+25 = 1+25+1 = 25+1+1 = 9+9+9. %e A008437 (End) %o A008437 (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 A008437 Equals A085121/8. %Y A008437 Cf. A000004 (the even bisection), A000196, A290081. %K A008437 nonn %O A008437 0,12 %A A008437 _N. J. A. Sloane_