A321209 Decimal expansion of the volume of the Löbell polyhedron L(5).

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

Offset

1,1

Links

Table of n, a(n) for n=1..100.

Taiyo Inoue, Organizing Volumes of Right-Angled Hyperbolic Polyhedra, arXiv:0809.2111 [math.GT], 2008.

Example

4.3062076007308086529198371598422094492411852354129341142249491178199...

Mathematica

theta[n_] := Pi/2 - ArcCos[1/(2 Cos[Pi/n])];
lambda[z_] := -Integrate[Log[Abs[2 Sin[t]]], {t, 0, z}];
vol[n_] := n/2 (2 lambda[theta[n]] + lambda[theta[n] + Pi/n] + lambda[theta[n] - Pi/n] - lambda[2 theta[n] - Pi/2]);
RealDigits[N[vol[5], 100] // Chop] // First

Crossrefs

Cf. A144222.

Sequence in context: A242721 A251610 A021703 * A139823 A307087 A019756

Adjacent sequences: A321206 A321207 A321208 * A321210 A321211 A321212

Keyword

nonn,cons

Author

Jean-François Alcover, Oct 30 2018

Status

approved