cp's OEIS Frontend

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

%I A217511 #22 Jun 05 2022 08:32:17
%S A217511 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,
%T A217511 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,
%U A217511 0,0,0,0,18
%N A217511 Theta series of hexagonal diamond or Lonsdaleite net with respect to an atom.
%C A217511 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
%H A217511 Andrey Zabolotskiy, <a href="/A217511/b217511.txt">Table of n, a(n) for n = 0..1000</a>
%H A217511 G. L. Hall, <a href="https://doi.org/10.1063/1.527833">Comment on the paper "Theta series and magic numbers for diamond and certain ionic crystal structures" [J. Math. Phys. 28, 1653 (1987)]</a>. Journal of Mathematical Physics; Sep. 1988, Vol. 29 Issue 9, pp. 2090-2092. - From _N. J. A. Sloane_, Dec 18 2012
%H A217511 N. J. A. Sloane, <a href="https://doi.org/10.1063/1.527472">Theta-Series and Magic Numbers for Diamond and Certain Ionic Crystal Structures</a>, J. Math. Phys., 28 (1987), pp. 1653-1657.
%H A217511 N. J. A. Sloane and Boon K. Teo, <a href="https://doi.org/10.1063/1.449551">Theta series and magic numbers for closepacked spherical clusters</a>, J. Chemical Phys 83, 6520-6534 (1985).
%F A217511 a(n) = A004012(n/8) + A005873(n), where the 1st term is 0 unless 8|n. - _Andrey Zabolotskiy_, Jun 03 2022
%Y A217511 Cf. A005925, A008264, A004012, A005873.
%K A217511 nonn
%O A217511 0,10
%A A217511 _N. J. A. Sloane_, Oct 05 2012
%E A217511 Missing a(71) = 0 inserted by _Andrey Zabolotskiy_, Jun 03 2022