A119412 a(n) = n*(n+11).
0, 12, 26, 42, 60, 80, 102, 126, 152, 180, 210, 242, 276, 312, 350, 390, 432, 476, 522, 570, 620, 672, 726, 782, 840, 900, 962, 1026, 1092, 1160, 1230, 1302, 1376, 1452, 1530, 1610, 1692, 1776, 1862, 1950, 2040, 2132, 2226, 2322, 2420, 2520
Offset: 0
Links
- Felix P. Muga II, Extending the Golden Ratio and the Binet-de Moivre Formula, Preprint on ResearchGate, March 2014.
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Programs
-
Mathematica
s=0;lst={s};Do[s+=n++ +12;AppendTo[lst, s], {n, 0, 7!, 2}];lst (* Vladimir Joseph Stephan Orlovsky, Nov 19 2008 *) Table[n(n+11),{n,0,100}] (* Vladimir Joseph Stephan Orlovsky, May 19 2011 *) LinearRecurrence[{3,-3,1},{0,12,26},50] (* Harvey P. Dale, Jun 11 2016 *) -
PARI
a(n)=n*(n+11) \\ Charles R Greathouse IV, Jan 21 2015
Formula
a(n) = 2*A056115(n). - Zerinvary Lajos, Feb 12 2007
a(n) = 2*a(n-1) - a(n-2) + 2 with a(0)=0, a(1)=12. - Vincenzo Librandi, Aug 01 2010
G.f.: 2*x*(-6+5*x)/(x-1)^3. - R. J. Mathar, Jul 14 2012
Sum_{n>=1} 1/a(n) = 83711/304920 via Sum_{n>=0} 1/((n+x)(n+y)) = (psi(x)-psi(y))/(x-y). - R. J. Mathar, Jul 14 2012
Sum_{n>=1} (-1)^(n+1)/a(n) = 2*log(2)/11 - 20417/304920. - Amiram Eldar, Jan 15 2021
From Elmo R. Oliveira, Dec 12 2024: (Start)
E.g.f.: exp(x)*x*(12 + x).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
Extensions
Definition simplified and the most obfuscating programs removed by R. J. Mathar, Jul 31 2010
Offset corrected (from 11 to 0) by Vincenzo Librandi, Aug 01 2010