

A245741


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


0



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
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)



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. 2125.


FORMULA

2*C/Pi + (1/2)*log(32*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_(31212)).
Sequence in context: A155158 A241140 A109986 * A175473 A180079 A019844
Adjacent sequences: A245738 A245739 A245740 * A245742 A245743 A245744


KEYWORD

nonn,cons,easy


AUTHOR

JeanFrançois Alcover, Jul 31 2014


STATUS

approved



