A008264 -id:A008264 - cp's OEIS frontend

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

N. J. A. Sloane, Oct 05 2012

nonn

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

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).

Cf. A005925, A008264, A004012, A005873.

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

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

A008524 Coordination sequence for 4-dimensional lonsdaleite (or wurtzite).

Original entry on oeis.org

1, 5, 20, 53, 116, 213, 360, 561, 832, 1171, 1600

Offset: 0

N. J. A. Sloane

M. O'Keeffe, N-dimensional diamond, sodalite and rare sphere packings, Acta Cryst., A 47 (1991), 749-753.

M. O'Keeffe, N-dimensional diamond, sodalite and rare sphere packings, Acta Cryst., A 47 (1991), 749-753.

For 3-D see A008264. Cf. A008525 etc.

Missing a(1)=5 inserted by Sean A. Irvine, Oct 17 2020

cp's OEIS Frontend

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

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