A249523 Decimal expansion of rho(a,b), the cross-correlation coefficient of two sides of a random Gaussian triangle in three dimensions.

2, 3, 7, 0, 5, 1, 0, 2, 5, 2, 0, 9, 6, 0, 0, 2, 8, 6, 5, 8, 5, 5, 6, 9, 5, 0, 4, 6, 7, 6, 4, 0, 8, 5, 7, 1, 9, 4, 0, 1, 7, 6, 9, 1, 6, 2, 3, 6, 9, 7, 8, 1, 3, 1, 8, 6, 3, 2, 3, 8, 2, 6, 4, 5, 8, 9, 6, 8, 3, 1, 0, 6, 2, 3, 1, 4, 3, 1, 6, 5, 3, 1, 1, 8, 4, 1, 4, 5, 3, 3, 9, 9, 3, 8, 5, 7, 3, 3, 6, 9, 4, 3, 3

Offset

0,1

Comments

Coordinates are independent normally distributed random variables with mean 0 and variance 1.

Links

Table of n, a(n) for n=0..102.

Steven R. Finch, Random Triangles, January 21, 2010. [Cached copy, with permission of the author]

Eric Weisstein's MathWorld, Gaussian Triangle Picking

Formula

rho = (-8 + 3*sqrt(3) + Pi)/(-8 + 3*Pi).

Example

0.237051025209600286585569504676408571940176916236978...

Mathematica

rho = (-8 + 3*Sqrt[3] + Pi)/(-8 + 3*Pi); RealDigits[rho, 10, 103] // First

Prog

(PARI) (sqrt(27)+Pi-8)/(3*Pi-8) \\ Charles R Greathouse IV, Apr 20 2016

Crossrefs

Cf. A102519, A102520, A102556, A102557, A102558, A102559, A249491, A249492.

Sequence in context: A117024 A263501 A203143 * A301316 A023048 A083521

Adjacent sequences: A249520 A249521 A249522 * A249524 A249525 A249526

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Oct 31 2014

Status

approved