cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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).

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%I A245736 #7 Jul 31 2014 05:33:50
%S A245736 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,
%T A245736 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,
%U A245736 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
%N 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).
%H A245736 Shu-Chiuan Chang and Robert Shrock, <a href="http://arxiv.org/abs/cond-mat/0602574">Some Exact Results for Spanning Trees on Lattices.</a>, Discrete Math., J. Phys. A: Math. Gen. 39, 5653-5658 (2006).
%F A245736 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.
%e A245736 0.786684275378832179121657989494695380551170816578...
%t A245736 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
%Y A245736 Cf. A218387(z_sq), A245725(z_tri).
%K A245736 nonn,cons,easy
%O A245736 0,1
%A A245736 _Jean-François Alcover_, Jul 31 2014