A217511 Theta series of hexagonal diamond or Lonsdaleite net with respect to an atom.

1, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 1, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 18

Offset: 0

Author

N. J. A. Sloane, Oct 05 2012

Keywords

• nonn

Comments

Eq. (20) of [Sloane, 1987] gives the g.f. of this sequence if one replaces the binomial in the round brackets with the factor eta_{3/8}(X^(16/3)); this error propagated from Eq. (67) of [Sloane & Teo, 1985], where the second curly brackets should be replaced by psi_{8/3}(q^(16/3)) to get the g.f. of A005873 (or, alternatively, replace the power 4/3 with 1/3 in both formulas). - Andrey Zabolotskiy, Jun 04 2022

Links

• Andrey Zabolotskiy, Table of n, a(n) for n = 0..1000
• G. L. Hall, Comment on the paper "Theta series and magic numbers for diamond and certain ionic crystal structures" [J. Math. Phys. 28, 1653 (1987)]. Journal of Mathematical Physics; Sep. 1988, Vol. 29 Issue 9, pp. 2090-2092. - From _N. J. A. Sloane_, Dec 18 2012
• N. J. A. Sloane, Theta-Series and Magic Numbers for Diamond and Certain Ionic Crystal Structures, J. Math. Phys., 28 (1987), pp. 1653-1657.
• N. J. A. Sloane and Boon K. Teo, Theta series and magic numbers for closepacked spherical clusters, J. Chemical Phys 83, 6520-6534 (1985).

Crossrefs

Cf. A005925, A008264, A004012, A005873.

Formula

a(n) = A004012(n/8) + A005873(n), where the 1st term is 0 unless 8|n. - Andrey Zabolotskiy, Jun 03 2022

Extensions

Missing a(71) = 0 inserted by Andrey Zabolotskiy, Jun 03 2022