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 A155212 a(n) = (n^2 + 9*n + 4)/2. 5
 2, 7, 13, 20, 28, 37, 47, 58, 70, 83, 97, 112, 128, 145, 163, 182, 202, 223, 245, 268, 292, 317, 343, 370, 398, 427, 457, 488, 520, 553, 587, 622, 658, 695, 733, 772, 812, 853, 895, 938, 982, 1027, 1073, 1120, 1168, 1217, 1267, 1318, 1370, 1423, 1477, 1532 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 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.: ( -2 - x + 2*x^2 )/(x - 1)^3 . - R. J. Mathar, Mar 23 2011 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Feb 26 2012 Sum_{n>=0} 1/a(n) = 271/280 + 2*Pi*tan(sqrt(65)*Pi/2)/sqrt(65). - Amiram Eldar, Dec 13 2022 MATHEMATICA Table[(n^2 + 9 n + 4)/2, {n, 0, 200}] (* Vladimir Joseph Stephan Orlovsky, Jun 12 2011 *) LinearRecurrence[{3, -3, 1}, {2, 7, 13}, 60] (* Harvey P. Dale, Aug 11 2014 *) PROG (Magma) I:=[2, 7, 13]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 26 2012 (PARI) for(n=0, 60, print1((n^2+9*n+4)/2", ")); \\ Vincenzo Librandi, Feb 26 2012 CROSSREFS Cf. A000217. Sequence in context: A344959 A295397 A329817 * A346870 A106675 A022946 Adjacent sequences: A155209 A155210 A155211 * A155213 A155214 A155215 KEYWORD nonn,easy AUTHOR Vincenzo Librandi, Jan 22 2009 EXTENSIONS Edited by Jon E. Schoenfield, Jun 23 2010 a(0)=2 from Vincenzo Librandi, Mar 22 2011 STATUS approved

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Last modified December 10 08:26 EST 2023. Contains 367701 sequences. (Running on oeis4.)