cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A016923 a(n) = (6*n + 1)^3.

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%I A016923 #27 Nov 01 2024 21:26:44
%S A016923 1,343,2197,6859,15625,29791,50653,79507,117649,166375,226981,300763,
%T A016923 389017,493039,614125,753571,912673,1092727,1295029,1520875,1771561,
%U A016923 2048383,2352637,2685619,3048625,3442951,3869893,4330747,4826809,5359375,5929741,6539203,7189057
%N A016923 a(n) = (6*n + 1)^3.
%D A016923 S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 1.6.3.
%H A016923 Vincenzo Librandi, <a href="/A016923/b016923.txt">Table of n, a(n) for n = 0..2000</a>
%H A016923 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A016923 Sum_{n>=0} 1/a(n) = Pi^3/(36*sqrt(3)) + 91*zeta(3)/216.
%F A016923 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - _Wesley Ivan Hurt_, Dec 28 2023
%F A016923 From _Stefano Spezia_, Nov 01 2024: (Start)
%F A016923 E.g.f.: exp(x)*(1 + 342*x + 756*x^2 + 216*x^3).
%F A016923 a(n) = A000578(A016921(n)). (End)
%t A016923 a[n_]:=(6*n + 1)^3; Array[a, 60, 0] (* or *)
%t A016923 LinearRecurrence[{4, -6, 4, -1}, {1, 343, 2197, 6859}, 60] (* or *)
%t A016923 CoefficientList[Series[(1 + 339 x + 831 x^2 + 125 x^3)/(-1 + x)^4, {x, 0, 60}], x] (* _Stefano Spezia_, Sep 03 2018 *)
%o A016923 (Magma) [(6*n+1)^3: n in [0..60]]; // _Vincenzo Librandi_, May 04 2011
%Y A016923 Cf. A000578, A016921.
%K A016923 nonn,easy
%O A016923 0,2
%A A016923 _N. J. A. Sloane_