A249456 Decimal expansion of a constant appearing in the expression of the asymptotic expected volume V(d) of the convex hull of uniformly selected n(d) points in the interior of a d-dimensional unit cube.

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

Offset

1,1

Links

Table of n, a(n) for n=1..103.

Steven R. Finch, Convex Lattice Polygons, December 18, 2003. [Cached copy, with permission of the author]

Formula

k = exp(log(2*Pi) - gamma - 1/2).

Lim_{d -> infinity} V(d) =

0 if n(d) <= (k - epsilon)^d

1 if n(d) >= (k + epsilon)^d

Example

2.139690947412859860505302263852352444323146956...

Mathematica

k = Exp[Log[2*Pi] - EulerGamma - 1/2]; RealDigits[k, 10, 103] // First

Crossrefs

Cf. A249455.

Sequence in context: A099644 A369446 A058113 * A234746 A359648 A237765

Adjacent sequences: A249453 A249454 A249455 * A249457 A249458 A249459

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Oct 29 2014

Status

approved