

A005886


Theta series of f.c.c. lattice with respect to tetrahedral hole.
(Formerly M3429)


6



4, 12, 12, 16, 24, 12, 24, 36, 12, 28, 36, 24, 36, 36, 24, 24, 60, 36, 28, 48, 12, 60, 60, 24, 48, 48, 36, 48, 60, 24, 52, 84, 48, 24, 60, 36, 48, 96, 36, 72, 48, 36, 72, 60, 48, 52, 96, 36, 60, 96, 24, 72, 108, 24, 48, 60, 72, 96, 84, 60, 48, 108, 36, 52, 72, 60, 108, 108, 36, 48, 108
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OFFSET

0,1


COMMENTS

Empirically, the number of integral quadruples with sum = 1, sumofsquares = 2n1.  Colin Mallows, Dec 31 2016


REFERENCES

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
G. Nebe and N. J. A. Sloane, Home page for this lattice
N. J. A. Sloane and B. K. Teo, Theta series and magic numbers for closepacked spherical clusters, J. Chem. Phys. 83 (1985) 65206534.
Index entries for sequences related to f.c.c. lattice


FORMULA

a(n) = 1/2 * A005878(n) = 2 * A005869(n) = 4 * A008443(n).  Michael Somos, May 31 2012


EXAMPLE

4 + 12*x + 12*x^2 + 16*x^3 + 24*x^4 + 12*x^5 + 24*x^6 + 36*x^7 + 12*x^8 + ...


MATHEMATICA

QP = QPochhammer; CoefficientList[4(QP[q^2]^2/QP[q])^3 + O[q]^50, q] (* JeanFrançois Alcover, Jul 04 2017, after Michael Somos *)


CROSSREFS

Cf. A005869, A005878, A008443. Partial sums is A121054. Cf also A278081A278086.
Sequence in context: A074258 A253137 A120213 * A096442 A211437 A195199
Adjacent sequences: A005883 A005884 A005885 * A005887 A005888 A005889


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane


EXTENSIONS

Terms a(50) onward added by G. C. Greubel, Feb 20 2018


STATUS

approved



