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%I #5 Jul 31 2014 10:46:17
%S 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,
%T 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,
%U 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
%N Decimal expansion of z_UJ, the bulk limit of the number of spanning trees on a Union Jack 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.
%F 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.
%F Equals 2*A245736.
%e 1.5733685507576643582433159789893907611023416331560654994372929...
%t 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
%Y Cf. A218387(z_sq), A245725(z_tri), A245736(z_br), A245737(z_hc), A245739(z_kag), A245740(z_(3-12-12)).
%K nonn,cons,easy
%O 1,2
%A _Jean-François Alcover_, Jul 31 2014