A364895 Decimal expansion of the 4-volume of the unit regular pentachoron (5-cell).

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

Offset

0,2

Links

Table of n, a(n) for n=0..99.

Polytope Wiki, Pentachoron.

Eric Weisstein's World of Mathematics, Pentatope.

Wikipedia, 5-cell.

Index entries for algebraic numbers, degree 2.

Formula

Equals sqrt(5)/96.

In general, the n-volume of the unit regular n-simplex is sqrt(n+1)/(n!*2^(n/2)).

Example

0.02329237476562280933...

Mathematica

First[RealDigits[Sqrt[5]/96, 10, 100, -1]] (* Paolo Xausa, Jun 12 2024 *)

Prog

(PARI) sqrt(5)/96

Crossrefs

Decimal expansion of 4-volumes: this sequence (5-cell), A000007 = 1 (8-cell or tesseract), A020793 = 1/6 (16-cell), A000038 = 2 (24-cell), A364896 (120-cell), A364897 (600-cell).

Decimal expansion of the n-volume of the unit regular n-simplex: A120011 (n=2), A020829 (n=3), this sequence (n=4).

Sequence in context: A349972 A163204 A389004 * A299619 A215269 A352485

Adjacent sequences: A364892 A364893 A364894 * A364896 A364897 A364898

Keyword

nonn,cons,changed

Author

Jianing Song, Aug 12 2023

Status

approved