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A245725
Decimal expansion of z_tri, a constant related to the enumeration of spanning trees on the triangular lattice (this is different from A242968).
6
1, 6, 1, 5, 3, 2, 9, 7, 3, 6, 0, 9, 7, 2, 5, 2, 5, 7, 0, 4, 6, 8, 1, 8, 2, 5, 5, 3, 6, 1, 9, 0, 3, 1, 9, 7, 0, 3, 6, 1, 2, 0, 9, 2, 0, 3, 9, 0, 2, 9, 3, 5, 0, 8, 0, 6, 5, 4, 3, 4, 2, 3, 5, 1, 8, 0, 5, 0, 7, 5, 5, 6, 4, 0, 3, 6, 3, 4, 9, 2, 1, 0, 4, 1, 8, 9, 3, 8, 0, 4, 5, 4, 4, 6, 8, 5, 6, 9, 6, 0, 3, 6, 7, 4
OFFSET
1,2
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.22 Lenz-Ising Constants, p. 400.
LINKS
Robert Shrock and F. Y. Wu, Spanning Trees on Graphs and Lattices in d Dimensions, arXiv:cond-mat/0004341 [cond-mat.stat-mech], 2000, p. 7.
FORMULA
Equals log(2) + log(3) + H, where H is the auxiliary constant A242967.
Equals Sum_{n>=1} 10*n*(arccoth((3*n) / 2) - 2 * arccoth(3*n)). - Antonio Graciá Llorente, Oct 13 2024
EXAMPLE
1.6153297360972525704681825536190319703612092039029350806543423518...
MATHEMATICA
H = Sqrt[3]/(6*Pi)*PolyGamma[1, 1/6] - Pi/Sqrt[3] - Log[6]; RealDigits[Log[2] + Log[3] + H, 10, 104] // First
(* or *) 3*(Sqrt[3]/Pi)*N[Sum[1/n^2 - 1/(n+4)^2, {n, 1, Infinity, 6}], 104] // RealDigits // First
CROSSREFS
KEYWORD
nonn,cons,easy,changed
AUTHOR
STATUS
approved