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

1,1

Comments

The triaugmented hexagonal prism is Johnson solid J_57.

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Wikipedia, Triaugmented hexagonal prism.

Formula

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

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

Example

3.3051829925398634646920138743636575896990438184040...

Mathematica

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

Crossrefs

Cf. A385259 (surface area + 7).

Cf. A010503, A104956, A385569, A385578.

Sequence in context: A377143 A256119 A388084 * A217552 A128046 A102899

Adjacent sequences: A385691 A385692 A385693 * A385695 A385696 A385697

Keyword

nonn,cons,easy

Author

Paolo Xausa, Jul 07 2025

Status

approved