

A004024


Theta series of b.c.c. lattice with respect to deep hole.
(Formerly M3227)


4



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
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OFFSET

0,1


REFERENCES

Ono and Skinner, Ann. Math., 147 (1998), 453470.
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 closepacked spherical clusters, J. Chem. Phys. 83 (1985) 65206534.


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[ (1q^(4k))^4 / (1q^k), {k, 1, max}], {q, 0, max}], q] (* JeanFrançois Alcover, Feb 10 2012, after A045831 *)
terms = 74; QP = QPochhammer; s = 4 QP[z^4]^4/QP[z] + O[z]^terms; CoefficientList[s, z] (* JeanFrançois 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



