A245741 Decimal expansion of z_UJ, the bulk limit of the number of spanning trees on a Union Jack lattice.

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

Offset

1,2

Links

Table of n, a(n) for n=1..104.

Robert Shrock and F. Y. Wu, Spanning Trees on Graphs and Lattices in d Dimensions pp. 21-25.

Formula

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

Equals 2*A245736.

Example

1.5733685507576643582433159789893907611023416331560654994372929...

Mathematica

z[UJ] = 2*Catalan/Pi + (1/2)*Log[3 - 2*Sqrt[2]] + (2/Pi)*Integrate[ArcTan[t]/t, {t, 0, 3 + 2*Sqrt[2]}]; RealDigits[N[Re[z[UJ]], 104]] // First

Crossrefs

Cf. A218387(z_sq), A245725(z_tri), A245736(z_br), A245737(z_hc), A245739(z_kag), A245740(z_(3-12-12)).

Sequence in context: A344111 A241140 A109986 * A175473 A180079 A019844

Adjacent sequences: A245738 A245739 A245740 * A245742 A245743 A245744

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Jul 31 2014

Status

approved