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

Author

Paolo Xausa, May 22 2025

Keywords

• nonn
• cons
• easy

Comments

The elongated pentagonal cupola is Johnson solid J_20.

Examples

			10.0182541612713266373651755525797920503105009319...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 2..10000
• Wikipedia, Elongated pentagonal cupola.

Crossrefs

Cf. A179591 (surface area - 10).

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

Programs

Mathematica

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

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.