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URL: https://oeis.org/A119412

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A119412
a(n) = n*(n+11).
4
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
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)
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
Sequence in context: A075689 A054303 A184826 * A105814 A297427 A357893
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