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 A242815 Decimal expansion of the expected number of returns to the origin of a random walk on a 7-d lattice. 2
 1, 0, 9, 3, 9, 0, 6, 3, 1, 5, 5, 8, 7, 8, 4, 7, 9, 9, 6, 6, 8, 3, 2, 7, 1, 8, 2, 3, 5, 5, 9, 0, 1, 9, 8, 6, 3, 7, 1, 1, 2, 8, 9, 9, 7, 7, 1, 6, 4, 9, 6, 1, 1, 5, 4, 4, 9, 1, 6, 8, 9, 0, 7, 3, 8, 8, 6, 1, 2, 6, 5, 4, 5, 7, 0, 5, 0, 8, 0, 5, 2, 2, 8, 4, 4, 8, 9, 5, 1, 9, 1, 9, 7, 2, 9, 8, 5, 5, 9, 8, 7, 5, 7, 2, 9, 9 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 REFERENCES Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.9 Polya's random walk constants, p. 323. LINKS Eric Weisstein's World of Mathematics, Polya's Random Walk Constants FORMULA m(d) = d/(2*Pi)^d*multipleIntegral(-Pi..Pi) (d-sum_(k=1..d) cos(t_k))^(-1) dt_1 dt_2 ... dt_d, where d is the lattice dimension. m(d) = integral_(t>0) exp(-t)*BesselI(0,t/d)^d dt where BesselI(0,x) is the zeroth modified Bessel function. EXAMPLE 1.09390631558784799668327... MAPLE m7:= int(exp(-t)*BesselI(0, t/7)^7, t=0..infinity): s:= convert(evalf(m7, 120), string): map(parse, subs("."=NULL, [seq(i, i=s)]))[]; # Alois P. Heinz, May 23 2014 MATHEMATICA d = 7; d/Pi^d*NIntegrate[(d - Sum[Cos[t[k]], {k, 1, d}])^-1, Sequence @@ Table[{t[k], 0, Pi}, {k, 1, d}] // Evaluate] // RealDigits[#, 10, 7]& // First CROSSREFS Cf. A086230, A086231, A086232, A086233, A086234, A086235, A086236, A242812, A242813, A242814, A242816. Sequence in context: A266559 A111971 A181045 * A155166 A159467 A198608 Adjacent sequences:  A242812 A242813 A242814 * A242816 A242817 A242818 KEYWORD nonn,cons AUTHOR Jean-François Alcover, May 23 2014 EXTENSIONS More terms from Alois P. Heinz, May 23 2014 STATUS approved

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Last modified June 19 16:48 EDT 2019. Contains 324222 sequences. (Running on oeis4.)