A384909 Decimal expansion of the volume of an elongated pentagonal orthobicupola with unit edge.

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

Offset

2,2

Comments

The elongated pentagonal orthobicupola is Johnson solid J_38.

Also the volume of an elongated pentagonal gyrobicupola (Johnson solid J_39) with unit edge.

Links

Paolo Xausa, Table of n, a(n) for n = 2..10000

Wikipedia, Elongated pentagonal gyrobicupola.

Wikipedia, Elongated pentagonal orthobicupola.

Formula

Equals (10 + 8*sqrt(5) + 15*sqrt(5 + 2*sqrt(5)))/6 = (10 + 8*A002163 + 15*sqrt(5 + A010476))/6.

Equals the largest root of 1296*x^4 - 8640*x^3 - 82440*x^2 - 109200*x + 76525.

Example

12.342299479604519768304624665067309540604246504993...

Mathematica

First[RealDigits[(10 + 8*Sqrt[5] + 15*Sqrt[5 + Sqrt[20]])/6, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J38", "Volume"], 10, 100]]

Crossrefs

Cf. A384625 (surface area - 10).

Cf. A002163, A010476, A384283, A384624, A384871.

Sequence in context: A264809 A035578 A227784 * A256445 A275103 A359729

Adjacent sequences: A384906 A384907 A384908 * A384910 A384911 A384912

Keyword

nonn,cons,easy

Author

Paolo Xausa, Jun 12 2025

Status

approved