A097321 - OEIS

%I #29 Feb 21 2025 05:19:05

%S 24,210,720,1716,3360,5814,9240,13800,19656,26970,35904,46620,59280,

%T 74046,91080,110544,132600,157410,185136,215940,249984,287430,328440,

%U 373176,421800,474474,531360,592620,658416,728910,804264,884640,970200,1061106,1157520

%N a(n) = (3*n-1) * 3*n * (3*n+1).

%H Vincenzo Librandi, <a href="/A097321/b097321.txt">Table of n, a(n) for n = 1..10000</a>

%H S. Ramanujan, <a href="http://www.imsc.res.in/~rao/ramanujan/NoteBooks/NoteBook2/chapterII/page2.htm">Notebook entry</a>.

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

%F G.f.: 6x * (4x^2 + 19x + 4) / (1-x)^4.

%F Sum_{n>=1} 1/a(n) = (log(3) - 1)/2. - _Amiram Eldar_, Jul 04 2020

%F Sum_{n>=1} (-1)^(n+1)/a(n) = 1/2 - 2*log(2)/3. - _Amiram Eldar_, May 15 2022

%F E.g.f.: 3*exp(x)*x*(8 + 27*x + 9*x^2). - _Stefano Spezia_, Feb 20 2025

%t Table[27n^3-3n,{n,40}]  (* _Harvey P. Dale_, Mar 30 2011 *)

%o (Magma) [27*n^3-3*n: n in [1..40]]; // _Vincenzo Librandi_, Sep 07 2011

%Y Cf. A069072, A069140, A002391, A016767.

%K nonn,easy

%O 1,1

%A _Ralf Stephan_, Aug 07 2004