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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
OFFSET
0,2
LINKS
FORMULA
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Oct 05 2012
EXTENSIONS
Name edited by Andrey Zabolotskiy, Jun 21 2022
STATUS
approved