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
Examples
1.5733685507576643582433159789893907611023416331560654994372929...
Links
- Robert Shrock and F. Y. Wu, Spanning Trees on Graphs and Lattices in d Dimensions pp. 21-25.
Crossrefs
Programs
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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
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.