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 A132764 a(n) = n*(n+22). 13
 0, 23, 48, 75, 104, 135, 168, 203, 240, 279, 320, 363, 408, 455, 504, 555, 608, 663, 720, 779, 840, 903, 968, 1035, 1104, 1175, 1248, 1323, 1400, 1479, 1560, 1643, 1728, 1815, 1904, 1995, 2088, 2183, 2280, 2379, 2480, 2583, 2688, 2795, 2904, 3015, 3128, 3243, 3360 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS G. C. Greubel, Table of n, a(n) for n = 0..5000 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*(n + 22). a(n) = 2*n + a(n-1) + 21 (with a(0)=0). - Vincenzo Librandi, Aug 03 2010 a(0)=0, a(1)=23, a(2)=48, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, May 02 2012 From Amiram Eldar, Jan 16 2021: (Start) Sum_{n>=1} 1/a(n) = H(22)/22 = A001008(22)/A102928(22) = 19093197/113809696, where H(k) is the k-th harmonic number. Sum_{n>=1} (-1)^(n+1)/a(n) = 156188887/5121436320. (End) From G. C. Greubel, Mar 14 2022: (Start) G.f.: x*(23 - 21*x)/(1-x)^3. E.g.f.: x*(23 + x)*exp(x). (End) EXAMPLE a(1)=2*1+0+21=23; a(2)=2*2+23+21=48; a(3)=2*3+48+21=75. - Vincenzo Librandi, Aug 03 2010 MATHEMATICA Table[n(n+22), {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 23, 48}, 50] (* Harvey P. Dale, May 02 2012 *) PROG (PARI) a(n)=n*(n+22) \\ Charles R Greathouse IV, Oct 07 2015 (Sage) [n*(n+22) for n in (0..50)] # G. C. Greubel, Mar 14 2022 CROSSREFS Cf. A001008, A002378, A005563, A028347, A028552, A028557, A028560, A028563, A028566, A028569, A098603, A098847, A098848, A098849, A098850, A102928, A120071, A132759, A132760, A132761, A132762, A132763, A132765, A132766, A132767. Sequence in context: A087807 A044100 A044481 * A029493 A063321 A176660 Adjacent sequences:  A132761 A132762 A132763 * A132765 A132766 A132767 KEYWORD easy,nonn AUTHOR Omar E. Pol, Aug 28 2007 STATUS approved

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Last modified June 26 18:18 EDT 2022. Contains 354885 sequences. (Running on oeis4.)