A377342 Decimal expansion of the volume of a truncated octahedron with unit edge length.

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

Offset

2,3

Comments

Length of the closed curve of Cartesian equation x^2 + y^2 = (1 + abs(y/x)/sqrt(1 + (y/x)^2))^2 (see Spezia link). - Stefano Spezia, Sep 09 2025

Links

Table of n, a(n) for n=2..91.

Stefano Spezia, Length of a Cartoony Round Cloud.

Eric Weisstein's World of Mathematics, Truncated Octahedron.

Wikipedia, Truncated octahedron.

Index entries for algebraic numbers, degree 2.

Formula

Equals 8*sqrt(2) = 8*A002193 = 4*A010466 = 2*A010487.

Equals Integral_{t=0..2*Pi} sqrt((1 + abs(sin(t)))^2 + cos(t)^2) (see Spezia link). - Stefano Spezia, Sep 09 2025

Example

11.3137084989847603904135097936775846285573750030...

Mathematica

First[RealDigits[8*Sqrt[2], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["TruncatedOctahedron", "Volume"], 10, 100]]

Prog

(PARI) 8*sqrt(2) \\ Charles R Greathouse IV, May 18 2026

Crossrefs

Cf. A377341 (surface area), A020797 (circumradius/10), A152623 (midradius).

Cf. A131594 (analogous for a regular octahedron).

Cf. A002193, A010466, A010487.

Sequence in context: A171961 A205121 A152903 * A226522 A122507 A257258

Adjacent sequences: A377339 A377340 A377341 * A377343 A377344 A377345

Keyword

nonn,cons,easy

Author

Paolo Xausa, Oct 25 2024

Status

approved