A140681 a(n) = 3*n*(n+6).
0, 21, 48, 81, 120, 165, 216, 273, 336, 405, 480, 561, 648, 741, 840, 945, 1056, 1173, 1296, 1425, 1560, 1701, 1848, 2001, 2160, 2325, 2496, 2673, 2856, 3045, 3240, 3441, 3648, 3861, 4080, 4305, 4536, 4773, 5016, 5265, 5520, 5781
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..5000
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Crossrefs
Programs
-
Maple
A140681:=n->3*n*(n+6); seq(A140681(n), n=0..100); # Wesley Ivan Hurt, Dec 10 2013
-
Mathematica
Table[3n(n+6), {n,0,100}] (* Wesley Ivan Hurt, Dec 10 2013 *) LinearRecurrence[{3,-3,1},{0,21,48},50] (* Harvey P. Dale, May 03 2023 *) -
PARI
a(n)=3*n*(n+6) \\ Charles R Greathouse IV, Jun 17 2017
Formula
a(n) = A028560(n)*3 = 3*n^2 + 18*n = n*(3*n+18).
a(n) = 6*n + a(n-1) + 15 with n>0, a(0)=0. - Vincenzo Librandi, Aug 03 2010
from G. C. Greubel, Jul 20 2017: (Start)
G.f.: 3*x*(7 - 5*x)/(1-x)^3.
E.g.f.: 3*x*(x+7)*exp(x). (End)
From Amiram Eldar, Feb 26 2022: (Start)
Sum_{n>=1} 1/a(n) = 49/360.
Sum_{n>=1} (-1)^(n+1)/a(n) = 37/1080. (End)