

A293237


Decimal expansion of the escape probability for a random walk on the 3D fcc lattice.


3



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, 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, 3, 3, 5, 6, 7, 3, 5, 3, 7, 6, 6, 8, 2, 2, 9, 6, 1, 1, 0
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OFFSET

0,1


COMMENTS

The return probability equals unity minus this constant. The expected number of visits to the origin is the inverse of this constant.
The escape probability for the hcp lattice also equals this constant. The escape probability for the diamond lattice is 3/4 times this constant.


LINKS



FORMULA

Equals 2^(14/3)*Pi^4/(9*Gamma(1/3)^6).


EXAMPLE

0.74368176349535122890496981936537648...


MATHEMATICA

RealDigits[2^(14/3)*Pi^4/(9*Gamma[1/3]^6), 10, 100][[1]] (* G. C. Greubel, Oct 26 2018 *)


PROG

(PARI) 2^(14/3)*Pi^4/(9*gamma(1/3)^6) \\ Altug Alkan, Apr 09 2018
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); 2^(14/3)*Pi(R)^4/(9*Gamma(1/3)^6); // G. C. Greubel, Oct 26 2018


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



