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

0,2

Links

Table of n, a(n) for n=0..45.

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).

Formula

Equals 2 * A056115. - 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

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 *)

Prog

(PARI) a(n)=n*(n+11) \\ Charles R Greathouse IV, Jan 21 2015

Crossrefs

Cf. A056115, A063930.

Sequence in context: A075689 A054303 A184826 * A105814 A297427 A357893

Adjacent sequences: A119409 A119410 A119411 * A119413 A119414 A119415

Keyword

easy,nonn

Author

Zerinvary Lajos, Jul 26 2006

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

Status

approved