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 A246966 Decimal expansion of H_2, the analog of Madelung's constant for the planar hexagonal lattice. 0
 1, 5, 4, 2, 2, 1, 9, 7, 2, 1, 7, 0, 6, 5, 0, 5, 2, 5, 8, 5, 3, 1, 4, 1, 5, 7, 6, 4, 3, 6, 4, 2, 4, 5, 2, 9, 5, 6, 1, 9, 4, 8, 0, 7, 3, 5, 9, 1, 3, 1, 5, 4, 7, 8, 5, 3, 8, 8, 1, 6, 4, 0, 1, 9, 0, 8, 6, 3, 2, 1, 8, 1, 9, 3, 6, 7, 6, 9, 6, 7, 4, 8, 2, 3, 3, 9, 1, 1, 3, 1, 8, 7, 4, 4, 3, 6, 8, 0, 7, 5, 0, 2, 3 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The ionic hexagonal (triangular) lattice considered here consists of three interpenetrating hexagonal lattices of ions with charges +1, -1, 0. Equivalently, one may consider the honeycomb net consisting of two hexagonal lattices of ions with charges +1 and -1 (the h-BN layer structure). In any case, this lattice sum is based on the nearest neighbor distance (not the length of the period of the ionic crystal structure, which is sqrt(3) times greater). - Andrey Zabolotskiy, Jun 21 2022 REFERENCES Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Sections 1.10 Madelung's constant, p. 78. LINKS Table of n, a(n) for n=1..103. David Borwein, Jonathan M. Borwein and Keith F. Taylor, Convergence of lattice sums and Madelung's constant, J. Math. Phys. 26 (1985), 2999-3009. Eric Weisstein's MathWorld, Madelung Constants FORMULA H_2 = (-3 + sqrt(3))*zeta(1/2)*((1 - sqrt(2))*zeta(1/2, 1/3) + zeta(1/2, 1/6)), where zeta(s,a) gives the generalized Riemann zeta function. EXAMPLE 1.54221972170650525853141576436424529561948... MATHEMATICA H2 = (-3 + Sqrt[3])*Zeta[1/2]*((1 - Sqrt[2])*Zeta[1/2, 1/3] + Zeta[1/2, 1/6]); RealDigits[H2, 10, 103] // First PROG (PARI) (sqrt(3)-3)*zeta(1/2)*((1-sqrt(2))*zetahurwitz(1/2, 1/3) + zetahurwitz(1/2, 1/6)) \\ Charles R Greathouse IV, Jan 31 2018 CROSSREFS Cf. A088537, A085469, A090734, A247040. Sequence in context: A242600 A102593 A090462 * A081749 A074825 A225063 Adjacent sequences: A246963 A246964 A246965 * A246967 A246968 A246969 KEYWORD nonn,cons,easy AUTHOR Jean-François Alcover, Sep 10 2014 STATUS approved

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Last modified December 6 18:41 EST 2023. Contains 367614 sequences. (Running on oeis4.)