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 A005878 Theta series of cubic lattice with respect to deep hole. (Formerly M4496) 6
 8, 24, 24, 32, 48, 24, 48, 72, 24, 56, 72, 48, 72, 72, 48, 48, 120, 72, 56, 96, 24, 120, 120, 48, 96, 96, 72, 96, 120, 48, 104, 168, 96, 48, 120, 72, 96, 192, 72, 144, 96, 72, 144, 120, 96, 104, 192, 72, 120, 192, 48, 144, 216, 48, 96, 120, 144, 192, 168, 120, 96, 216, 72 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Number of ways of writing 8*n+3 as the sum of three odd squares. - Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 23 2008 Expansion of Jacobi theta constant theta_2^3. - Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 23 2008 REFERENCES J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 107. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..99 from Herman Jamke (hermanjamke(AT)fastmail.fm)) G. Nebe and N. J. A. Sloane, Home page for this lattice FORMULA G.f.: Form (Sum_{n=-inf..inf} q^((2n+1)^2))^3, then divide by q^3 and set q = x^(1/8). a(n) = 8 * A008443(n). MATHEMATICA QP = QPochhammer; CoefficientList[(2 QP[q^2]^2/QP[q])^3 + O[q]^63, q] (* Jean-François Alcover, Jul 04 2017 *) PROG (PARI) {a(n)=if(n<0, 0, 8*polcoeff( sum(k=0, (sqrtint(8*n+1)-1)\2, x^((k^2+k)/2), x*O(x^n))^3, n))} {a(n)=local(A); if(n<0, 0, A=x*O(x^n); 8*polcoeff( (eta(x^2+A)^2/eta(x+A))^3, n))} \\ Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 23 2008 CROSSREFS Equals 8 times A008443. Cf. A085121. Sequence in context: A263630 A205376 A088448 * A128637 A280708 A109272 Adjacent sequences:  A005875 A005876 A005877 * A005879 A005880 A005881 KEYWORD nonn,easy AUTHOR EXTENSIONS More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 23 2008 STATUS approved

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Last modified October 22 18:31 EDT 2019. Contains 328319 sequences. (Running on oeis4.)