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
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).
Programs
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Magma
[27*n^3-3*n: n in [1..40]]; // Vincenzo Librandi, Sep 07 2011
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Mathematica
Table[27n^3-3n,{n,40}] (* Harvey P. Dale, Mar 30 2011 *)
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
E.g.f.: 3*exp(x)*x*(8 + 27*x + 9*x^2). - Stefano Spezia, Feb 20 2025