A163758 a(n) = 9*n*(n+1).

0, 18, 54, 108, 180, 270, 378, 504, 648, 810, 990, 1188, 1404, 1638, 1890, 2160, 2448, 2754, 3078, 3420, 3780, 4158, 4554, 4968, 5400, 5850, 6318, 6804, 7308, 7830, 8370, 8928, 9504, 10098, 10710, 11340, 11988, 12654, 13338, 14040, 14760, 15498, 16254, 17028

Offset

0,2

Comments

18 times the n-th triangular number.

Numbers of the form 36*m^2 + 18*m, where m = 0,-1,1,-2,2,-3,3,... - Bruno Berselli, Apr 07 2013

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

G.f.: 18*x/(1-x)^3.

a(n) = 18*A000217(n) = 9*A002378(n).

E.g.f.: 9*x*(x + 2)*exp(x). - G. C. Greubel, Aug 02 2017

From Amiram Eldar, Feb 22 2023: (Start)

Sum_{n>=1} 1/a(n) = 1/9.

Sum_{n>=1} (-1)^(n+1)/a(n) = (2*log(2) - 1)/9.

Product_{n>=1} (1 - 1/a(n)) = -(9/Pi)*cos(sqrt(13)*Pi/6).

Product_{n>=1} (1 + 1/a(n)) = (9/Pi)*cos(sqrt(5)*Pi/6). (End)

Mathematica

Table[9 n (n + 1), {n, 0, 100}] (* Vladimir Joseph Stephan Orlovsky, Jun 26 2011 *)

Prog

(Magma) [0] cat [36*m^2+18*m where m is n*t: t in [-1, 1], n in [1..20]]; // Bruno Berselli, Apr 07 2013
(PARI) a(n)=9*n*(n+1) \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. A000217, A002378.

Sequence in context: A044120 A056808 A044501 * A232546 A069973 A272138

Adjacent sequences: A163755 A163756 A163757 * A163759 A163760 A163761

Keyword

nonn,easy

Author

Vincenzo Librandi, Aug 03 2009

Extensions

a(35) inserted by R. J. Mathar, Aug 06 2009

Status

approved