cp's OEIS Frontend

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

%I A245725 #22 Oct 31 2024 01:49:32
%S A245725 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,
%T A245725 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,
%U A245725 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
%N A245725 Decimal expansion of z_tri, a constant related to the enumeration of spanning trees on the triangular lattice (this is different from A242968).
%D A245725 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.22 Lenz-Ising Constants, p. 400.
%H A245725 Vincenzo Librandi, <a href="/A245725/b245725.txt">Table of n, a(n) for n = 1..1000</a>
%H A245725 Robert Shrock and F. Y. Wu, <a href="http://arxiv.org/abs/cond-mat/0004341">Spanning Trees on Graphs and Lattices in d Dimensions</a>, arXiv:cond-mat/0004341 [cond-mat.stat-mech], 2000, p. 7.
%F A245725 Equals log(2) + log(3) + H, where H is the auxiliary constant A242967.
%F A245725 Equals Sum_{n>=1} 10*n*(arccoth((3*n) / 2) - 2 * arccoth(3*n)). - _Antonio Graciá Llorente_, Oct 13 2024
%e A245725 1.6153297360972525704681825536190319703612092039029350806543423518...
%t A245725 H = Sqrt[3]/(6*Pi)*PolyGamma[1, 1/6] - Pi/Sqrt[3] - Log[6]; RealDigits[Log[2] + Log[3] + H, 10, 104] // First
%t A245725 (* or *) 3*(Sqrt[3]/Pi)*N[Sum[1/n^2 - 1/(n+4)^2, {n, 1, Infinity, 6}], 104] // RealDigits // First
%Y A245725 Cf. A242967, A242968, A242969.
%K A245725 nonn,cons,easy
%O A245725 1,2
%A A245725 _Jean-François Alcover_, Jul 30 2014