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a(n) = 8*n^3 - 6*n - 1.
0

%I #20 Mar 02 2024 14:01:43

%S -1,1,51,197,487,969,1691,2701,4047,5777,7939,10581,13751,17497,21867,

%T 26909,32671,39201,46547,54757,63879,73961,85051,97197,110447,124849,

%U 140451,157301,175447,194937,215819,238141,261951,287297,314227,342789,373031,405001

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

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

%H Proofwiki, <a href="https://proofwiki.org/wiki/Trisecting_the_Angle_by_Compass_and_Straightedge_Construction_is_Impossible">Trisecting the Angle by Compass and Straightedge Construction is Impossible</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Angle_trisection">Angle trisection</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

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

%t Table[8n^3-6n-1,{n,0,37}] (* _James C. McMahon_, Feb 05 2024 *)

%Y Cf. A144129.

%K sign,easy

%O 0,3

%A _DarĂ­o Clavijo_, Feb 05 2024