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 A098850 a(n) = n*(n + 18). 21
 0, 19, 40, 63, 88, 115, 144, 175, 208, 243, 280, 319, 360, 403, 448, 495, 544, 595, 648, 703, 760, 819, 880, 943, 1008, 1075, 1144, 1215, 1288, 1363, 1440, 1519, 1600, 1683, 1768, 1855, 1944, 2035, 2128, 2223, 2320, 2419, 2520, 2623, 2728, 2835, 2944, 3055 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Felix P. Muga II, Extending the Golden Ratio and the Binet-de Moivre Formula, Preprint on ResearchGate, March 2014. Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n) = (n+9)^2 - 9^2 = n*(n + 18), n>=0. G.f.: x*(19 - 17*x)/(1-x)^3. a(n) = 2*n + a(n-1) + 17 (with a(0)=0). - Vincenzo Librandi, Nov 17 2010 From G. C. Greubel, Jul 29 2016: (Start) a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). E.g.f.: x*(19 + x)*exp(x). (End) From Amiram Eldar, Jan 16 2021: (Start) Sum_{n>=1} 1/a(n) = H(18)/18 = A001008(18)/A102928(18) = 14274301/73513440, where H(k) is the k-th harmonic number. Sum_{n>=1} (-1)^(n+1)/a(n) = 1632341/44108064. (End) MAPLE seq(n*(n+18), n=0..52); # Emeric Deutsch, Mar 06 2005 MATHEMATICA LinearRecurrence[{3, -3, 1}, {0, 19, 40}, 25] (* G. C. Greubel, Jul 29 2016 *) PROG (PARI) a(n)=n*(n+18) \\ Charles R Greathouse IV, Jun 17 2017 CROSSREFS Cf. A001008, A098832, A102928. a(n-9), n>=10, ninth column (used for the n=9 series of the hydrogen atom) of triangle A120070. Sequence in context: A041716 A041718 A041720 * A264537 A164078 A128677 Adjacent sequences:  A098847 A098848 A098849 * A098851 A098852 A098853 KEYWORD nonn,easy AUTHOR Eugene McDonnell (eemcd(AT)mac.com), Nov 04 2004 EXTENSIONS More terms from Emeric Deutsch, Mar 06 2005 STATUS approved

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Last modified May 20 11:16 EDT 2022. Contains 353871 sequences. (Running on oeis4.)