A173309 a(n) = 19*n*(n+1).

0, 38, 114, 228, 380, 570, 798, 1064, 1368, 1710, 2090, 2508, 2964, 3458, 3990, 4560, 5168, 5814, 6498, 7220, 7980, 8778, 9614, 10488, 11400, 12350, 13338, 14364, 15428, 16530, 17670, 18848, 20064, 21318, 22610, 23940, 25308, 26714, 28158, 29640

Offset

0,2

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

a(n) = 38*A000217(n).

a(0)=0, a(1)=38, a(2)=114, a(n)=3*a(n-1)-3*a(n-2)+a(n-3). - Harvey P. Dale, Oct 12 2012

a(0)=0, a(n)=a(n-1) +38*n. - Vincenzo Librandi, Oct 13 2012

G.f.: 38*x/(1-x)^3. - Vincenzo Librandi, Oct 13 2012

From Amiram Eldar, Feb 22 2023: (Start)

Sum_{n>=1} 1/a(n) = 1/19.

Sum_{n>=1} (-1)^(n+1)/a(n) = (2*log(2) - 1)/19.

Product_{n>=1} (1 - 1/a(n)) = -(19/Pi)*cos(sqrt(23/19)*Pi/2).

Product_{n>=1} (1 + 1/a(n)) = (19/Pi)*cos(sqrt(15/19)*Pi/2). (End)

Mathematica

Table[19n(n+1), {n, 0, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 38, 114}, 40] (* Harvey P. Dale, Oct 12 2012 *)
CoefficientList[Series[38*x/(1-x)^3, {x, 0, 100}], x] (* Vincenzo Librandi, Oct 13 2012 *)

Prog

(Magma) I:=[0, 38, 114]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..40]]; // Vincenzo Librandi, Oct 13 2012
(PARI) a(n)=19*n*(n+1) \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. A000217.

Sequence in context: A283804 A251229 A282850 * A044289 A044670 A118633

Adjacent sequences: A173306 A173307 A173308 * A173310 A173311 A173312

Keyword

nonn,easy

Author

Vincenzo Librandi, Feb 16 2010

Extensions

Incorrect formulas and examples removed by R. J. Mathar, Jan 04 2011

Status

approved