A102557 Denominator of the probability that 2n-dimensional Gaussian random triangle has an obtuse angle.

4, 32, 512, 4096, 131072, 1048576, 16777216, 134217728, 8589934592, 68719476736, 1099511627776, 8796093022208, 281474976710656, 2251799813685248, 36028797018963968, 288230376151711744, 36893488147419103232, 295147905179352825856, 4722366482869645213696, 37778931862957161709568

Offset

1,1

Comments

Presumably this is the same as A093581? - Andrew S. Plewe, Apr 18 2007

Links

Robert Israel, Table of n, a(n) for n = 1..830

Eric Weisstein's World of Mathematics, Gaussian Triangle Picking

Formula

From Robert Israel, Sep 29 2016: (Start)

a(n) is the denominator of p(n) = Sum_{k=n..2n-1} binomial(2n-1,k) 3^(2n-k)/4^(2n-1).

-(6n+3)p(n)+(14n+11)p(n+1)-(8n+8)p(n+2)=0 for n >= 1.

G.f. of p(n): 3x(1-1/sqrt(4-3x))/(2-2x). (End)

Example

3/4, 15/32, 159/512, 867/4096, 19239/131072, 107985/1048576, ...

Maple

p:= gfun:-rectoproc({(-6*n-3)*v(n)+(14*n+11)*v(n+1)+(-8*n-8)*v(n+2), v(0) = 0, v(1) = 3/4, v(2) = 15/32}, v(n), remember):
seq(denom(p(n)), n=1..50); # Robert Israel, Sep 29 2016

Mathematica

a[n_] := (3^n/4^(2n-1)) Binomial[2n-1, n] Hypergeometric2F1[1, 1-n, 1+n, -1/3] // Denominator; Array[a, 20] (* Jean-François Alcover, Mar 22 2019 *)

Prog

(PARI) a(n) = denominator(sum(k=n, 2*n-1, binomial(2*n-1, k)*3^(2*n-k)/4^(2*n-1))); \\ Michel Marcus, Mar 23 2019

Crossrefs

Cf. A093581, A102556, A102558, A102559.

Sequence in context: A192501 A192487 A093581 * A144935 A153511 A140179

Adjacent sequences: A102554 A102555 A102556 * A102558 A102559 A102560

Keyword

nonn,frac

Author

Eric W. Weisstein, Jan 14 2005

Status

approved