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A340002 Random walk in R^3: Numerators of the expected distance after n steps. 2

%I

%S 0,1,4,13,28,1199,239,113149,1487,14345663,292223,17110600987,

%T 14849671,545242142639,961780559,1704615588759647,856088316689,

%U 7836371329207844977,1103759659545457,16895087931630048788047,59954362566895631,2699144613568894213138579,28918424475964028179

%N Random walk in R^3: Numerators of the expected distance after n steps.

%C 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.

%C 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.

%H Ludovic Schwob, <a href="/A340002/b340002.txt">Table of n, a(n) for n = 0..59</a>

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

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

%Y See A340003 for denominators.

%K nonn,frac

%O 0,3

%A _Ludovic Schwob_, Dec 26 2020

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Last modified September 16 18:26 EDT 2021. Contains 347473 sequences. (Running on oeis4.)