A293237 - OEIS

A293237

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

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

G. C. Greubel, Table of n, a(n) for n = 0..10000

Shunya Ishioka and Masahiro Koiwa, Random walks on diamond and hexagonal close packed lattices, Phil. Mag. A, 37 (1978), 517-533.

G. L. Montet, Integral methods in the calculation of correlation factors in diffusion, Phys. Rev. B 7 (1973), 650-662.

Index entries for sequences related to f.c.c. lattice

Index entries for sequences related to walks

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

Cf. A242761, A293238.

Sequence in context: A244817 A303612 A306555 * A316250 A199727 A255168

Adjacent sequences: A293234 A293235 A293236 * A293238 A293239 A293240

KEYWORD

nonn,cons

AUTHOR

Andrey Zabolotskiy, Oct 03 2017

STATUS

approved