A384214 - OEIS

A384214

Decimal expansion of the volume of a gyroelongated square cupola with unit edge.

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

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OFFSET

1,1

COMMENTS

The gyroelongated square cupola is Johnson solid J_23.

LINKS

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

Wikipedia, Gyroelongated square cupola.

FORMULA

Equals 1 + (2/3)*sqrt(2) + (2/3)*sqrt(4 + 2*sqrt(2) + 2*sqrt(146 + 103*sqrt(2))) = 1 + A010466/3 + (2/3)*sqrt(4 + A010466 + 2*sqrt(146 + 103*A002193)).

Equals the largest real root of 6561*x^8 - 52488*x^7 + 113724*x^6 - 9720*x^5 - 1616922*x^4 + 396360*x^3 + 1537020*x^2 - 178632*x - 3391.

EXAMPLE

6.21076579203920003665822883345980731696010032091...

MATHEMATICA

First[RealDigits[1 + Sqrt[8]/3 + 2/3*Sqrt[4 + Sqrt[8] + 2*Sqrt[146 + 103*Sqrt[2]]], 10, 100]] (* or *)

First[RealDigits[PolyhedronData["J23", "Volume"], 10, 100]]

CROSSREFS

Cf. A384215 (surface area).

Cf. A002193, A010466, A179587, A179638, A384142.

Sequence in context: A120002 A296432 A171542 * A335587 A320302 A284761

Adjacent sequences: A384211 A384212 A384213 * A384215 A384216 A384217

KEYWORD

nonn,cons,easy

AUTHOR

Paolo Xausa, May 23 2025

STATUS

approved