0,1

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.

Table of n, a(n) for n=0..86.

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

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

0.74368176349535122890496981936537648...

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

Cf. A242761, A293238.

Sequence in context: A243309 A244817 A303612 * A199727 A255168 A257776

Adjacent sequences: A293234 A293235 A293236 * A293238 A293239 A293240

nonn,cons

Andrey Zabolotskiy, Oct 03 2017

approved