A384143 Decimal expansion of the volume of an elongated triangular cupola with unit edge.

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

Offset: 1

Author

Paolo Xausa, May 22 2025

Keywords

• nonn
• cons
• easy

Comments

The elongated triangular cupola is Johnson solid J_18.

Examples

			3.776587513330895147625910115766890282555601110196...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Wikipedia, Elongated triangular cupola.

Crossrefs

Cf. A384141 (surface area - 4).

Cf. A002193, A002194, A344078, A383852, A384139.

Programs

Mathematica

First[RealDigits[(5*Sqrt[2] + 9*Sqrt[3])/6, 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J18", "Volume"], 10, 100]]

Formula

Equals (5*sqrt(2) + 9*sqrt(3))/6 = (5*A002193 + 9*A002194)/6.

Equals the largest root of 1296*x^4 - 21096*x^2 + 37249.