A245725 Decimal expansion of z_tri, a constant related to the enumeration of spanning trees on the triangular lattice (this is different from A242968).

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

Author

Jean-François Alcover, Jul 30 2014

Keywords

• nonn
• cons
• easy

Examples

			1.6153297360972525704681825536190319703612092039029350806543423518...
		

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.22 Lenz-Ising Constants, p. 400.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• 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.

Crossrefs

Cf. A242967, A242968, A242969.

Programs

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

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