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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).
3
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, 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, 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
OFFSET
0,1
LINKS
Shu-Chiuan Chang and Robert Shrock, Some Exact Results for Spanning Trees on Lattices., Discrete Math., J. Phys. A: Math. Gen. 39, 5653-5658 (2006).
FORMULA
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.
EXAMPLE
0.786684275378832179121657989494695380551170816578...
MATHEMATICA
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
CROSSREFS
Cf. A218387(z_sq), A245725(z_tri).
Sequence in context: A242816 A333566 A093827 * A088660 A244263 A288023
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved