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

0,2

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).

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)

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 *)

Prog

(PARI) a(n)=3*n*(n+6) \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. A028560, A033428, A045944, A140676, A067725, A140677, A140678, A067707, A140679, A140680, A140689, A000217, A005563, A067728, A140091, A212331.

Sequence in context: A156966 A146705 A146713 * A262423 A020178 A347372

Adjacent sequences: A140678 A140679 A140680 * A140682 A140683 A140684

Keyword

nonn,easy

Author

Omar E. Pol, May 22 2008

Status

approved