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A132771 a(n) = n*(n + 29).

%I A132771 #32 Oct 18 2024 15:44:24
%S A132771 0,30,62,96,132,170,210,252,296,342,390,440,492,546,602,660,720,782,
%T A132771 846,912,980,1050,1122,1196,1272,1350,1430,1512,1596,1682,1770,1860,
%U A132771 1952,2046,2142,2240,2340,2442,2546,2652,2760,2870,2982,3096,3212,3330,3450,3572
%N A132771 a(n) = n*(n + 29).
%H A132771 G. C. Greubel, <a href="/A132771/b132771.txt">Table of n, a(n) for n = 0..5000</a>
%H A132771 Felix P. Muga II, <a href="https://www.researchgate.net/publication/267327689_Extending_the_Golden_Ratio_and_the_Binet-de_Moivre_Formula">Extending the Golden Ratio and the Binet-de Moivre Formula</a>, Preprint on ResearchGate, March 2014.
%H A132771 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A132771 a(n) = 2*n + a(n-1) + 28 (with a(0)=0). - _Vincenzo Librandi_, Aug 03 2010
%F A132771 From _Amiram Eldar_, Jan 16 2021: (Start)
%F A132771 Sum_{n>=1} 1/a(n) = H(29)/29 = A001008(29)/A102928(29) = 9227046511387/67543597321200, where H(k) is the k-th harmonic number.
%F A132771 Sum_{n>=1} (-1)^(n+1)/a(n) = 2*log(2)/29 - 236266661971/9649085331600. (End)
%F A132771 From _G. C. Greubel_, Mar 13 2022: (Start)
%F A132771 G.f.: 2*(15*x - 14*x^2)/(1-x)^3.
%F A132771 E.g.f.: x*(30 + x)*exp(x). (End)
%t A132771 Table[n(n+29), {n,0,50}] (* _Bruno Berselli_, Apr 03 2015 *)
%t A132771 LinearRecurrence[{3,-3,1},{0,30,62},50] (* _Harvey P. Dale_, Oct 18 2024 *)
%o A132771 (PARI) a(n)=n*(n+29) \\ _Charles R Greathouse IV_, Jun 17 2017
%o A132771 (Sage) [n*(n+29) for n in (0..50)] # _G. C. Greubel_, Mar 13 2022
%Y A132771 Cf. A001008, A002378, A005563, A028347, A028552, A028557, A028560, A028563, A028566, A028569.
%Y A132771 Cf. A098849, A098850, A098603, A098847, A098848, A102928, A120071, A132759, A132760, A132761.
%Y A132771 Cf. A132762, A132763, A132764, A132765, A132766, A132767, A132768, A132769, A132770.
%K A132771 easy,nonn
%O A132771 0,2
%A A132771 _Omar E. Pol_, Aug 28 2007