A369922 a(n) = 8*n^3 - 6*n - 1.

-1, 1, 51, 197, 487, 969, 1691, 2701, 4047, 5777, 7939, 10581, 13751, 17497, 21867, 26909, 32671, 39201, 46547, 54757, 63879, 73961, 85051, 97197, 110447, 124849, 140451, 157301, 175447, 194937, 215819, 238141, 261951, 287297, 314227, 342789, 373031, 405001

Offset: 0

Author

Darío Clavijo, Feb 05 2024

Keywords

• sign
• easy
• changed

Comments

This polynomial (evaluated over the rationals) arises in demonstrating the impossibility of trisecting an arbitrary angle by compass and straightedge.

Links

• Proofwiki, Trisecting the Angle by Compass and Straightedge Construction is Impossible.
• Wikipedia, Angle trisection.
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A144129.

Programs

Mathematica

Table[8n^3-6n-1,{n,0,37}] (* James C. McMahon, Feb 05 2024 *)

Formula

a(n) = 2*A144129(n) - 1.

From Elmo R. Oliveira, Sep 04 2025: (Start)

G.f.: (-1 + 5*x + 41*x^2 + 3*x^3)/(-1+x)^4.

E.g.f.: (-1 + 2*x + 24*x^2 + 8*x^3)*exp(x).

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End)