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A004024 Theta series of b.c.c. lattice with respect to deep hole.
(Formerly M3227)
5
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; text; internal format)
OFFSET

0,1

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.

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

FORMULA

4*eta(32z)^4/eta(8z) = 4*Sum q^(x^2+2y^2+2z^2), x, y, z >= 1 and odd.

MATHEMATICA

max = 73; 4*CoefficientList[ Series[ Product[ (1-q^(4k))^4 / (1-q^k), {k, 1, max}], {q, 0, max}], q] (* Jean-François Alcover, Feb 10 2012, after A045831 *)

terms = 74; QP = QPochhammer; s = 4 QP[z^4]^4/QP[z] + O[z]^terms; CoefficientList[s, z] (* Jean-François Alcover, Jul 07 2017 *)

CROSSREFS

Equals 4*A045831.

Sequence in context: A172022 A152967 A301705 * A292276 A278083 A086663

Adjacent sequences:  A004021 A004022 A004023 * A004025 A004026 A004027

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified September 20 22:20 EDT 2018. Contains 315247 sequences. (Running on oeis4.)