A385694 Decimal expansion of the volume of a triaugmented hexagonal prism with unit edge.

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

Offset: 1

Author

Paolo Xausa, Jul 07 2025

Keywords

• nonn
• cons
• easy

Comments

The triaugmented hexagonal prism is Johnson solid J_57.

Examples

			3.3051829925398634646920138743636575896990438184040...
		

Links

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

Crossrefs

Cf. A385259 (surface area + 7).

Cf. A010503, A104956, A385569, A385578.

Programs

Mathematica

First[RealDigits[1/Sqrt[2] + 3*Sqrt[3]/2, 10, 100]]
First[RealDigits[PolyhedronData["J57", "Volume"], 10, 100]]

Formula

Equals 1/sqrt(2) + 3*sqrt(3)/2 = A010503 + A104956.

Equals the largest root of 16*x^4 - 232*x^2 + 625.