A385262 Decimal expansion of the volume of a gyroelongated pentagonal cupolarotunda with unit edge.

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

Offset

2,2

Comments

The gyroelongated pentagonal cupolarotunda is Johnson solid J_47.

Links

Paolo Xausa, Table of n, a(n) for n = 2..10000

Wikipedia, Gyroelongated pentagonal cupolarotunda.

Formula

Equals (5/12)*(11 + 5*sqrt(5) + 2*sqrt(2*(sqrt(650 + 290*sqrt(5)) - sqrt(5) - 1))) = (5/12)*(11 + 5*A002163 + 2*sqrt(2*(sqrt(650 + 290*A002163) - A002163 - 1))).

Equals the largest real root of 1679616*x^8 - 61585920*x^7 + 851472000*x^6 - 5108832000*x^5 + 4745790000*x^4 + 21346200000*x^3 - 29019375000*x^2 - 4576875000*x - 405859375.

Example

15.991096162004890063062980011720804055694009940053...

Mathematica

First[RealDigits[5/12*(11 + 5*# + 2*Sqrt[2*(Sqrt[650 + 290*#] - # - 1)]) & [Sqrt[5]], 10, 100]] (* or *)
First[RealDigits[PolyhedronData["J47", "Volume"], 10, 100]]

Crossrefs

Cf. A385263 (surface area).

Cf. A002163, A384283, A385256, A385258, A385260.

Sequence in context: A063623 A085566 A076390 * A321632 A397292 A147818

Adjacent sequences: A385259 A385260 A385261 * A385263 A385264 A385265

Keyword

nonn,cons,easy

Author

Paolo Xausa, Jun 27 2025

Status

approved