A385509 Decimal expansion of the volume of an augmented pentagonal prism with unit edge.

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

Offset: 1

Author

Paolo Xausa, Jul 01 2025

Keywords

• nonn
• cons
• easy

Comments

The augmented pentagonal prism is Johnson solid J_52.

Examples

			1.9561796609844827642259600980902259458356528159...
		

Links

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

Crossrefs

Cf. A385510 (surface area).

Cf. A002163.

Programs

Mathematica

First[RealDigits[Sqrt[233 + 90*Sqrt[5] + 12*Sqrt[50 + 20*Sqrt[5]]]/12, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J52", "Volume"], 10, 100]]

Formula

Equals sqrt(233 + 90*sqrt(5) + 12*sqrt(50 + 20*sqrt(5)))/12 = sqrt(233 + 90*A002163 + 12*sqrt(50 + 20*A002163))/12.

Equals the largest root of 429981696*x^8 - 2782937088*x^6 + 4776205824*x^4 - 1630792512*x^2 + 43414921.