A384213 Decimal expansion of the volume of an elongated pentagonal rotunda with unit edge.

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

Offset: 2

Author

Paolo Xausa, May 23 2025

Keywords

• nonn
• cons
• easy

Comments

The elongated pentagonal rotunda is Johnson solid J_21.

Examples

			14.611971811062835576338722470794915893557631368294...
		

Links

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

Crossrefs

Cf. A179637 (surface area - 10).

Cf. A002163, A010476, A384138, A384140, A384144.

Programs

Mathematica

First[RealDigits[(45 + 17*Sqrt[5] + 30*Sqrt[5 + Sqrt[20]])/12, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J21", "Volume"], 10, 100]]

Formula

Equals (45 + 17*sqrt(5) + 30*sqrt(5 + 2*sqrt(5)))/12 = (45 + 17*A002163 + 30*sqrt(5 + A010476))/12.

Equals the largest real root of 1296*x^4 - 19440*x^3 + 2340*x^2 + 70200*x + 43525.