A385264 Decimal expansion of the volume of a gyroelongated pentagonal birotunda with unit edge.
2, 0, 5, 8, 4, 8, 1, 3, 8, 1, 1, 7, 9, 6, 3, 9, 9, 0, 0, 2, 0, 3, 6, 5, 2, 6, 9, 2, 9, 9, 3, 5, 9, 2, 7, 8, 9, 8, 9, 4, 1, 1, 4, 0, 3, 7, 6, 4, 2, 8, 6, 4, 5, 8, 9, 4, 7, 3, 4, 5, 8, 6, 4, 9, 0, 2, 2, 6, 5, 6, 2, 2, 1, 0, 9, 4, 3, 4, 6, 4, 1, 5, 5, 7, 6, 0, 5, 2, 0, 6
Offset: 2
Examples
20.5848138117963990020365269299359278989411403764...
Links
- Paolo Xausa, Table of n, a(n) for n = 2..10000
- Wikipedia, Gyroelongated pentagonal birotunda.
Programs
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Mathematica
First[RealDigits[(45 + 17*# + 5*Sqrt[2*(Sqrt[650 + 290*#] - # - 1)])/6 & [Sqrt[5]], 10, 100]] (* or *) First[RealDigits[PolyhedronData["J48", "Volume"], 10, 100]]
Formula
Equals (45 + 17*sqrt(5) + 5*sqrt(2*(sqrt(650 + 290*sqrt(5)) - sqrt(5) - 1)))/6 = (45 + 17*A002163 + 5*sqrt(2*(sqrt(650 + 290*A002163) - A002163 - 1)))/6.
Equals the largest real root of 6561*x^8 - 393660*x^7 + 9316620*x^6 - 108207900*x^5 + 601832025*x^4 - 1417189500*x^3 + 965841750*x^2 + 597667500*x - 668786875.
Comments