A027691 a(n) = n^2 + n + 6.
6, 8, 12, 18, 26, 36, 48, 62, 78, 96, 116, 138, 162, 188, 216, 246, 278, 312, 348, 386, 426, 468, 512, 558, 606, 656, 708, 762, 818, 876, 936, 998, 1062, 1128, 1196, 1266, 1338, 1412, 1488, 1566, 1646, 1728, 1812, 1898, 1986, 2076, 2168, 2262, 2358, 2456, 2556
Offset: 0
Links
- Muniru A Asiru, Table of n, a(n) for n = 0..2000
- Patrick De Geest, Palindromic Quasi_Over_Squares of the form n^2+(n+X).
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Programs
-
GAP
List([0..50],n->n^2+n+6); # Muniru A Asiru, Jul 15 2018
-
Mathematica
Table[n^2+n+6,{n,0,100}] (* Vladimir Joseph Stephan Orlovsky, Mar 12 2011 *) -
PARI
a(n)=n^2+n+6 \\ Charles R Greathouse IV, Jun 17 2017
Formula
a(n) = 2*n + a(n-1), with a(0)=6. - Vincenzo Librandi, Aug 05 2010
Sum_{n>=0} 1/a(n) = Pi*tanh(Pi*sqrt(23)/2)/sqrt(23). - Amiram Eldar, Jan 17 2021
From Elmo R. Oliveira, Oct 28 2024: (Start)
G.f.: 2*(3 - 5*x + 3*x^2)/(1 - x)^3.
E.g.f.: (2*(3 + x) + x^2)*exp(x).
a(n) = 2*A152950(n+1). (End)
Extensions
Offset changed by Charles R Greathouse IV, Jul 25 2010