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A293237 Decimal expansion of the escape probability for a random walk on the 3D fcc lattice. 2
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 (list; constant; graph; refs; listen; history; text; internal format)
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

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.

FORMULA

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

EXAMPLE

0.74368176349535122890496981936537648...

CROSSREFS

Cf. A242761, A293238.

Sequence in context: A194705 A243309 A244817 * A199727 A255168 A257776

Adjacent sequences:  A293234 A293235 A293236 * A293238 A293239 A293240

KEYWORD

nonn,cons

AUTHOR

Andrey Zabolotskiy, Oct 03 2017

STATUS

approved

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Last modified February 24 21:33 EST 2018. Contains 299628 sequences. (Running on oeis4.)