A383852 Decimal expansion of the volume of an elongated triangular pyramid with unit edge.

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

Offset

0,1

Comments

The elongated triangular pyramid is Johnson solid J_7.

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

Wikipedia, Elongated triangular pyramid.

Formula

Equals (sqrt(2) + 3*sqrt(3))/12 = (A002193 + A010482)/12.

Minimal polynomial: 20736*x^4 - 8352*x^2 + 625. - Stefano Spezia, May 19 2025

Example

0.55086383208997724411533564572727626494984063640067...

Mathematica

First[RealDigits[(Sqrt[2] + Sqrt[27])/12, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J7", "Volume"], 10, 100]]

Crossrefs

Cf. A165663 (surface area).

Cf. A002193, A010482.

Sequence in context: A200516 A233383 A144184 * A119380 A121212 A182787

Adjacent sequences: A383849 A383850 A383851 * A383853 A383854 A383855

Keyword

nonn,cons,easy

Author

Paolo Xausa, May 19 2025

Status

approved