A005888 Theta series of hexagonal close-packing with respect to edge between layers. (Formerly M0008)

0, 0, 0, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 2, 0, 4, 0, 0, 0, 4, 0, 2, 0, 0, 0, 4, 0, 4, 0, 0, 0, 4, 0, 4, 0, 0, 0, 2, 0, 4, 0, 0, 0, 4, 0, 8, 0, 0, 0, 4, 0, 4, 0, 0, 0, 4, 0, 8, 0, 0, 0, 6, 0, 8, 0, 0, 0, 0, 0, 6, 0, 0, 0, 4, 0, 8, 0, 0, 0, 4, 0, 4, 0, 0, 0, 4, 0, 12, 0, 0, 0, 4, 0, 12, 0, 0, 0, 0, 0, 8, 0, 0, 0, 8, 0, 12, 0, 0, 0, 4, 0, 8, 0, 0, 0, 4, 0, 8, 0, 0, 0, 4, 0, 12

Offset

0,4

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Sean A. Irvine, Table of n, a(n) for n = 0..999

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.

Formula

Expansion of theta2(q^(4/3)) * (theta2(q^2)*psi(3, q^6) + theta3(q^2)*psi(6, q^6)) in q^(1/6) where psi(k, q) = Sum_{m=-infinity..infinity} q^((m+1/k)^2) and theta2 and theta3 are Jacobi theta functions [From Sloane and Teo]. - Sean A. Irvine, Sep 25 2016

Crossrefs

Sequence in context: A325787 A005929 A005871 * A213902 A170770 A107499

Adjacent sequences: A005885 A005886 A005887 * A005889 A005890 A005891

Keyword

easy,nonn

Author

N. J. A. Sloane.

Extensions

More terms from Sean A. Irvine, Sep 25 2016

Status

approved