|
%I #21 Sep 08 2022 08:46:19
%S 7,4,3,6,8,1,7,6,3,4,9,5,3,5,1,2,2,8,9,0,4,9,6,9,8,1,9,3,6,5,3,7,6,4,
%T 8,0,5,0,9,6,0,2,2,5,0,9,0,5,1,2,1,7,0,5,6,6,2,0,4,4,3,9,3,4,0,1,9,4,
%U 3,3,5,6,7,3,5,3,7,6,6,8,2,2,9,6,1,1,0
%N Decimal expansion of the escape probability for a random walk on the 3D fcc lattice.
%C The return probability equals unity minus this constant. The expected number of visits to the origin is the inverse of this constant.
%C The escape probability for the hcp lattice also equals this constant. The escape probability for the diamond lattice is 3/4 times this constant.
%H G. C. Greubel, <a href="/A293237/b293237.txt">Table of n, a(n) for n = 0..10000</a>
%H Shunya Ishioka and Masahiro Koiwa, <a href="https://doi.org/10.1080/01418617808239187">Random walks on diamond and hexagonal close packed lattices</a>, Phil. Mag. A, 37 (1978), 517-533.
%H G. L. Montet, <a href="https://doi.org/10.1103/PhysRevB.7.650">Integral methods in the calculation of correlation factors in diffusion</a>, Phys. Rev. B 7 (1973), 650-662.
%H <a href="/index/Fa#fcc">Index entries for sequences related to f.c.c. lattice</a>
%H <a href="/index/Wa#WALKS">Index entries for sequences related to walks</a>
%F Equals 2^(14/3)*Pi^4/(9*Gamma(1/3)^6).
%e 0.74368176349535122890496981936537648...
%t RealDigits[2^(14/3)*Pi^4/(9*Gamma[1/3]^6), 10, 100][[1]] (* _G. C. Greubel_, Oct 26 2018 *)
%o (PARI) 2^(14/3)*Pi^4/(9*gamma(1/3)^6) \\ _Altug Alkan_, Apr 09 2018
%o (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); 2^(14/3)*Pi(R)^4/(9*Gamma(1/3)^6); // _G. C. Greubel_, Oct 26 2018
%Y Cf. A242761, A293238.
%K nonn,cons
%O 0,1
%A _Andrey Zabolotskiy_, Oct 03 2017
|
