The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A173309 a(n) = 19*n*(n+1). 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 (list; graph; refs; listen; history; text; internal format)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 11 08:42 EDT 2024. Contains 375814 sequences. (Running on oeis4.)