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%I #22 Mar 11 2018 05:57:40
%S 1,2,8,5,8,4,6,5,4,9,7,5,4,7,7,9,4,5,8,6,3,1,3,8,5,1,6,1,1,1,6,5,3,2,
%T 4,3,7,9,1,0,9,9,5,5,1,2,0,7,6,6,8,8,0,3,4,9,6,7,1,0,9,4,9,8,4,8,5,0,
%U 7,9,0,0,4,5,5,2,6,6,2,3,1,4,6,8,3,4,9,7,9,0,5,7,1,6,4,6,2,4,5,3,0,5,6,9,3
%N Decimal expansion of Sum_{m,n,p = -infinity..infinity} 4*(-1)^(m + n + p)/sqrt(m^2 + (2n-1/2)^2 + (2p-1/2)^2).
%H I. J. Zucker, <a href="http://dx.doi.org/10.1088/0305-4470/9/4/006">Functional equations for poly-dimensional zeta functions and the evaluation of Madelung constants</a>, J. Phys. A: Math. Gen. 9 (4) (1976) 499, variable j(1).
%H I. J. Zucker, <a href="http://dx.doi.org/10.1088/0305-4470/8/11/008">Madelung constants and lattice sums for invariant cubic lattice complexes and certain tetragonal structures</a>, J. Phys. A: Math. Gen. 8 (11) (1975) 1734, variable j(1).
%F Equals 8*Sum_{n>=1, p>=1} cosech(d*Pi)/d where d = sqrt((n-1/2)^2 + 2*(p-1/2)^2).
%e 1.285846549754779458631385161116...
%t digits = 105; Clear[f]; f[n_, p_] := f[n, p] = (d = Sqrt[(n - 1/2)^2 + 2*(p - 1/2)^2]; (Csch[d*Pi]/d) // N[#, digits + 10] &); f[m_] := f[m] = 8*Sum[f[n, p], {n, 1, m}, {p, 1, m}] // RealDigits[#, 10, digits + 10] & // First; f[0]; f[m = 10]; While[ f[m] != f[m - 10], Print[m]; m = m + 10]; f[m][[1 ;; digits]] (* _Jean-François Alcover_, Feb 21 2013 *)
%Y Cf. A185576, A185577, A185578, A185579, A185580, A185581, A185582.
%K nonn,cons
%O 1,2
%A _R. J. Mathar_, Jan 31 2011
%E More terms from _Jean-François Alcover_, Feb 21 2013
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