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 A164136 a(n) = 11*n*(n+1). 2
 0, 22, 66, 132, 220, 330, 462, 616, 792, 990, 1210, 1452, 1716, 2002, 2310, 2640, 2992, 3366, 3762, 4180, 4620, 5082, 5566, 6072, 6600, 7150, 7722, 8316, 8932, 9570, 10230, 10912, 11616, 12342, 13090, 13860, 14652, 15466, 16302, 17160, 18040, 18942, 19866, 20812 (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) = 22*A000217(n) = 11*A002378(n). a(n) = 22*n + a(n-1) with n>0, a(0)=0. - Vincenzo Librandi, Nov 30 2010 G.f.: 22*x/(1-x)^3. - Vincenzo Librandi, Sep 12 2013 a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). - Vincenzo Librandi, Sep 12 2013 E.g.f.: 11*x*(2 + x)*exp(x). - G. C. Greubel, Sep 12 2017 From Amiram Eldar, Feb 22 2023: (Start) Sum_{n>=1} 1/a(n) = 1/11. Sum_{n>=1} (-1)^(n+1)/a(n) = (2*log(2) - 1)/11. Product_{n>=1} (1 - 1/a(n)) = -(11/Pi)*cos(sqrt(15/11)*Pi/2). Product_{n>=1} (1 + 1/a(n)) = (11/Pi)*cos(sqrt(7/11)*Pi/2). (End) MATHEMATICA CoefficientList[Series[(22 x) / (1 - x)^3, {x, 0, 40}], x] (* Vincenzo Librandi, Sep 12 2013 *) PROG (Magma) [11*n*(n+1): n in [0..40]]; // Vincenzo Librandi, Sep 12 2013 (PARI) a(n)=11*n*(n+1) \\ Charles R Greathouse IV, Jun 17 2017 CROSSREFS Cf. A000217, A002378. Sequence in context: A136604 A064710 A246415 * A041946 A303858 A041948 Adjacent sequences: A164133 A164134 A164135 * A164137 A164138 A164139 KEYWORD nonn,easy AUTHOR Vincenzo Librandi, Aug 11 2009 EXTENSIONS Offset corrected by R. J. Mathar, Aug 21 2009 STATUS approved

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Last modified September 7 22:13 EDT 2024. Contains 375749 sequences. (Running on oeis4.)