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

Offset: 0

Author

Andrey Zabolotskiy, Oct 03 2017

Keywords

• nonn
• cons

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.

Examples

			0.74368176349535122890496981936537648...
		

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

Crossrefs

Cf. A242761, A293238.

Programs

Magma

SetDefaultRealField(RealField(100)); R:= RealField(); 2^(14/3)*Pi(R)^4/(9*Gamma(1/3)^6); // G. C. Greubel, Oct 26 2018

Mathematica

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

PARI

2^(14/3)*Pi^4/(9*gamma(1/3)^6) \\ Altug Alkan, Apr 09 2018

Formula

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