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Search: id:A005878
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| A005878 |
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Theta series of cubic lattice with respect to deep hole.
(Formerly M4496)
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+0
3
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| 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; listen)
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OFFSET
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0,1
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COMMENT
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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
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 107.
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LINKS
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Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 23 2008, Table of n, a(n) for n = 0..99
G. Nebe and N. J. A. Sloane, Home page for this lattice
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FORMULA
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G.f.: Form (Sum_{n=-inf..inf} q^((2n+1)^2))^3, then divide by q^3 and set q = x^(1/8).
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PROGRAM
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(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
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CROSSREFS
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Equals 8 times A008443, Cf. A085121.
Equals 8*A008443. Cf. A085121.
Sequence in context: A099274 A036562 A088448 this_sequence A128637 A109272 A052349
Adjacent sequences: A005875 A005876 A005877 this_sequence A005879 A005880 A005881
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Feb 23 2008
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