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

0,10

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).

Formula

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

Crossrefs

Cf. A005925, A008264, A004012, A005873.

Sequence in context: A124856 A061858 A005873 * A307380 A178990 A276570

Adjacent sequences: A217508 A217509 A217510 * A217512 A217513 A217514

Keyword

nonn

Author

N. J. A. Sloane, Oct 05 2012

Extensions

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

Status

approved