A245740 - OEIS

%I #5 Jul 31 2014 10:46:57

%S 7,2,0,5,6,3,3,2,2,8,6,6,5,7,7,1,0,6,0,7,7,3,6,4,5,2,0,6,2,7,9,5,7,5,

%T 5,2,4,2,2,3,8,3,5,1,9,3,3,2,3,6,7,0,4,2,3,8,3,6,1,4,0,9,6,1,5,2,7,9,

%U 1,4,7,4,1,6,0,4,3,5,9,9,0,3,2,0,4,4,7,9,4,6,3,9,2,2,9,4,7,7,6,6,5,9,2

%N Decimal expansion of z_(3-12-12), the bulk limit of the number of spanning trees on a 3-12-12 lattice.

%H 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> pp. 21-25.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Truncated_hexagonal_tiling">Truncated hexagonal tiling</a>

%F (1/6)*(log(2) + 2*log(3) + log(5) + H), where H is the auxiliary constant A242967.

%F Equals (1/6)*(A245725 + log(15)).

%e 0.720563322866577106077364520627957552422383519332367042383614...

%t H = Sqrt[3]/(6*Pi)*PolyGamma[1, 1/6] - Pi/Sqrt[3] - Log[6]; RealDigits[(1/6)*(Log[2] + 2*Log[3] + Log[5] + H), 10, 103] // First

%Y Cf. A218387(z_sq), A242967(H), A245725(z_tri), A245736(z_br), A245737(z_hc), A245739(z_kag).

%K nonn,cons,easy

%O 0,1

%A _Jean-François Alcover_, Jul 31 2014