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%I #25 Oct 13 2022 06:37:21
%S 0,6,0,0,6,0,0,12,0,0,0,0,0,12,0,0,6,0,0,12,0,0,0,0,0,6,0,0,12,0,0,12,
%T 0,0,0,0,0,12,0,0,0,0,0,12,0,0,0,0,0,18,0,0,12,0,0,0,0,0,0,0,0,12,0,0,
%U 6,0,0,12,0,0,0,0,0,12,0,0,12,0,0,12,0,0,0,0,0,0,0,0,0,0,0,24,0,0,0,0,0,12,0,0,6,0,0,12,0
%N Theta series of planar hexagonal net (honeycomb) with respect to deep hole.
%H G. C. Greubel, <a href="/A217219/b217219.txt">Table of n, a(n) for n = 0..2500</a>
%H N. J. A. Sloane, <a href="http://dx.doi.org/10.1063/1.527472">Theta series and magic numbers for diamond and certain ionic crystal structures</a>, J. Math. Phys. 28 (1987), 1653-1657.
%F See A033685, A045833.
%F a(n) = 2*A033685(n) = 6*A045833(n).
%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 4*Pi/(3*sqrt(3)) = 2.418399... (A275486). - _Amiram Eldar_, Oct 13 2022
%t terms = 105; s = 6 q QPochhammer[q^9]^3/QPochhammer[q^3] + O[q]^(terms+5); CoefficientList[s, q][[1 ;; terms]] (* _Jean-François Alcover_, Jul 06 2017, after _Michael Somos_ *)
%t CoefficientList[Series[6 q QPochhammer[q^9]^3/QPochhammer[q^3], {q, 0, 100}], q] (* _G. C. Greubel_, Aug 10 2018 *)
%o (PARI) my(q='q+O('q^100)); concat([0], Vec(6*q*eta(q^9)^3/eta(q^3))) \\ _G. C. Greubel_, Aug 10 2018
%Y Cf. A033685, A045833, A275486.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Oct 05 2012
%E Name edited by _Andrey Zabolotskiy_, Jun 21 2022
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