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A004024
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Theta series of b.c.c. lattice with respect to deep hole.
(Formerly M3227)
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2
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4, 4, 8, 12, 4, 12, 12, 12, 16, 16, 8, 8, 28, 12, 20, 24, 8, 16, 28, 12, 16, 28, 20, 32, 20, 16, 16, 32, 20, 24, 28, 8, 36, 44, 12, 32, 36, 16, 24, 20, 28, 20, 56, 28, 16, 40, 20, 40, 44, 12, 36, 40, 20, 32, 40, 16, 24, 60, 32, 36, 40, 24, 32, 60, 24, 40, 24, 20, 60, 36, 24, 32, 56, 32
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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REFERENCES
| Ono and Skinner, Ann. Math., 147 (1998), 453-470.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane and B. K. Teo, Theta series and magic numbers for close-packed spherical clusters, J. Chem. Phys. 83 (1985) 6520-6534.
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..1000
G. Nebe and N. J. A. Sloane, Home page for this lattice
Index entries for sequences related to b.c.c. lattice
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FORMULA
| 4*eta(32z)^4/eta(8z) = 4*Sum q^(x^2+2y^2+2z^2), x, y, z >= 1 and odd.
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MATHEMATICA
| max = 73; 4*CoefficientList[ Series[ Product[ (1-q^(4k))^4 / (1-q^k), {k, 1, max}], {q, 0, max}], q] (* From Jean-François Alcover, Feb 10 2012, after A045831 *)
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CROSSREFS
| 4*A045831.
Sequence in context: A014687 A172022 A152967 * A086663 A003829 A194697
Adjacent sequences: A004021 A004022 A004023 * A004025 A004026 A004027
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KEYWORD
| nonn,easy,nice,changed
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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