A386740 Decimal expansion of the volume of an augmented sphenocorona with unit edges.

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

Offset

1,2

Comments

The augmented sphenocorona is Johnson solid J_87.

Links

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

Wikipedia, Augmented sphenocorona.

Formula

Equals sqrt(1 + 3*sqrt(3/2) + sqrt(13 + 3*sqrt(6)))/2 + 1/(3*sqrt(2)) = sqrt(1 + 3*A115754 + sqrt(13 + A010507))/2 + A020775.

Equals A386739 + A020775.

Equals the largest real root of 45137758519296*x^16 - 110336743047168*x^14 - 191069246324736*x^12 + 209269081571328*x^10 + 364547659290624*x^8 - 58793017190400*x^6 + 3306865979520*x^4 - 1275399855936*x^2 + 1439671249.

Example

1.7510539003719224011954274331734292512511481527...

Mathematica

First[RealDigits[Sqrt[1 + 3*Sqrt[3/2] + Sqrt[13 + Sqrt[54]]]/2 + 1/Sqrt[18], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J87", "Volume"], 10, 100]]

Crossrefs

Cf. A010502 (surface area - 1).

Cf. A010507, A020775, A115754, A386739, A386741.

Sequence in context: A021855 A397295 A350544 * A396261 A256846 A336698

Adjacent sequences: A386737 A386738 A386739 * A386741 A386742 A386743

Keyword

nonn,cons,easy

Author

Paolo Xausa, Aug 01 2025

Status

approved