A384144 Decimal expansion of the volume of an elongated pentagonal cupola with unit edge.

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

Offset

2,5

Comments

The elongated pentagonal cupola is Johnson solid J_20.

Links

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

Wikipedia, Elongated pentagonal cupola.

Formula

Equals (5 + 4*sqrt(5) + 15*sqrt(5 + 2*sqrt(5)))/6 = (5 + A010532 + 15*sqrt(5 + A010476))/6.

Equals the largest root of 324*x^4 - 1080*x^3 - 20340*x^2 - 18600*x + 49975.

Example

10.0182541612713266373651755525797920503105009319...

Mathematica

First[RealDigits[(5 + Sqrt[80] + 15*Sqrt[5 + Sqrt[20]])/6, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J20", "Volume"], 10, 100]]

Crossrefs

Cf. A179591 (surface area - 10).

Cf. A010476, A010532, A384138, A384140, A384213.

Sequence in context: A243370 A388389 A179048 * A388437 A173158 A379339

Adjacent sequences: A384141 A384142 A384143 * A384145 A384146 A384147

Keyword

nonn,cons,easy

Author

Paolo Xausa, May 22 2025

Status

approved