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 A217219 Theta series of planar hexagonal net (honeycomb) with respect to deep hole. 4
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS G. C. Greubel, Table of n, a(n) for n = 0..2500 N. J. A. Sloane, Theta series and magic numbers for diamond and certain ionic crystal structures, J. Math. Phys. 28 (1987), 1653-1657. FORMULA See A033685, A045833. a(n) = 2*A033685(n) = 6*A045833(n). 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 MATHEMATICA 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 *) CoefficientList[Series[6 q QPochhammer[q^9]^3/QPochhammer[q^3], {q, 0, 100}], q] (* G. C. Greubel, Aug 10 2018 *) PROG (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 CROSSREFS Cf. A033685, A045833, A275486. Sequence in context: A114760 A261508 A344182 * A113555 A066604 A081550 Adjacent sequences: A217216 A217217 A217218 * A217220 A217221 A217222 KEYWORD nonn AUTHOR N. J. A. Sloane, Oct 05 2012 EXTENSIONS Name edited by Andrey Zabolotskiy, Jun 21 2022 STATUS approved

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Last modified September 9 14:16 EDT 2024. Contains 375764 sequences. (Running on oeis4.)