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A340002 Random walk in R^3: Numerators of the expected distance after n steps. 2
0, 1, 4, 13, 28, 1199, 239, 113149, 1487, 14345663, 292223, 17110600987, 14849671, 545242142639, 961780559, 1704615588759647, 856088316689, 7836371329207844977, 1103759659545457, 16895087931630048788047, 59954362566895631, 2699144613568894213138579, 28918424475964028179 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The random variables X_n are defined by X_0=0 and X_(n+1)=X_n+U_n where U_n are i.i.d. random variables with uniform distribution on the 2-dimensional sphere. Then a(n)=E(|X_n|), take numerators.

Let (V_n)_n be i.i.d. random variables with uniform distribution on the interval [-2,2]. Then a(n)=E(|V_1+...+V_n|), take numerators.

LINKS

Ludovic Schwob, Table of n, a(n) for n = 0..59

FORMULA

a(n)/A340003(n) ~ 2*sqrt(2*n)/sqrt(3*Pi).

EXAMPLE

0, 1, 4/3, 13/8, 28/15, 1199/576, 239/105, 113149/46080, 1487/567, 14345663/5160960, ... = A340002/A340003.

CROSSREFS

See A340003 for denominators.

Sequence in context: A155331 A155387 A155366 * A135039 A168559 A212247

Adjacent sequences:  A339998 A340000 A340001 * A340003 A340004 A340005

KEYWORD

nonn,frac

AUTHOR

Ludovic Schwob, Dec 26 2020

STATUS

approved

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Last modified July 25 02:57 EDT 2021. Contains 346282 sequences. (Running on oeis4.)