A097321 a(n) = (3*n-1) * 3*n * (3*n+1).

24, 210, 720, 1716, 3360, 5814, 9240, 13800, 19656, 26970, 35904, 46620, 59280, 74046, 91080, 110544, 132600, 157410, 185136, 215940, 249984, 287430, 328440, 373176, 421800, 474474, 531360, 592620, 658416, 728910, 804264, 884640, 970200, 1061106, 1157520

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

S. Ramanujan, Notebook entry.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

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

Sum_{n>=1} 1/a(n) = (log(3) - 1)/2. - Amiram Eldar, Jul 04 2020

Sum_{n>=1} (-1)^(n+1)/a(n) = 1/2 - 2*log(2)/3. - Amiram Eldar, May 15 2022

Mathematica

Table[27n^3-3n, {n, 40}]  (* Harvey P. Dale, Mar 30 2011 *)

Prog

(Magma) [27*n^3-3*n: n in [1..40]]; // Vincenzo Librandi, Sep 07 2011

Crossrefs

Cf. A069072, A069140, A002391, A016767.

Sequence in context: A283540 A047659 A108671 * A105946 A050222 A169635

Adjacent sequences: A097318 A097319 A097320 * A097322 A097323 A097324

Keyword

nonn,easy

Author

Ralf Stephan, Aug 07 2004

Status

approved