A384138 Decimal expansion of the volume of an elongated pentagonal pyramid with unit edge.

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

Offset: 1

Author

Paolo Xausa, May 20 2025

Keywords

• nonn
• cons
• easy

Comments

The elongated pentagonal pyramid is Johnson solid J_9.

Examples

			2.0219802329847914934427275469190794425507332683273...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Wikipedia, Elongated pentagonal pyramid.

Crossrefs

Cf. A179553 (surface area - 5).

Cf. A002163, A383852, A384139, A384140.

Programs

Mathematica

First[RealDigits[(5 + Sqrt[5] + 6*Sqrt[25 + 10*Sqrt[5]])/24, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J9", "Volume"], 10, 100]]

Formula

Equals (5 + sqrt(5) + 6*sqrt(25 + 10*sqrt(5)))/24 = (5 + A002163 + 6*sqrt(25 + 10*A002163))/24.

Equals the largest root of 20736*x^4 - 17280*x^3 - 59760*x^2 + 15600*x + 9025.