A245736 Decimal expansion of z_br = z_4.8.8, the bulk limit of the number of spanning trees on a "bathroom" lattice (squares and octagons).

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

Offset

0,1

Links

Table of n, a(n) for n=0..102.

Shu-Chiuan Chang and Robert Shrock, Some Exact Results for Spanning Trees on Lattices., Discrete Math., J. Phys. A: Math. Gen. 39, 5653-5658 (2006).

Formula

C/Pi + (1/4)*log(3-2*sqrt(2)) + (1/Pi)*integral_{0..3+2*sqrt(2)} arctan(t)/t dt, where C is Catalan's constant.

Example

0.786684275378832179121657989494695380551170816578...

Mathematica

z[br] = Catalan/Pi + (1/4)*Log[3-2*Sqrt[2]] + (1/Pi)*Integrate[ArcTan[t]/t, {t, 0, 3+2*Sqrt[2]}]; RealDigits[N[Re[z[br]], 103]] // First

Crossrefs

Cf. A218387(z_sq), A245725(z_tri).

Sequence in context: A242816 A333566 A093827 * A088660 A244263 A288023

Adjacent sequences: A245733 A245734 A245735 * A245737 A245738 A245739

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Jul 31 2014

Status

approved