Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #33 Mar 13 2022 03:31:21
%S 0,27,56,87,120,155,192,231,272,315,360,407,456,507,560,615,672,731,
%T 792,855,920,987,1056,1127,1200,1275,1352,1431,1512,1595,1680,1767,
%U 1856,1947,2040,2135,2232,2331,2432,2535,2640,2747,2856,2967,3080,3195,3312,3431
%N a(n) = n*(n + 26).
%H G. C. Greubel, <a href="/A132768/b132768.txt">Table of n, a(n) for n = 0..5000</a>
%H 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 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = n*(n + 26).
%F a(n) = 2*n + a(n-1) + 25, with a(0)=0. - _Vincenzo Librandi_, Aug 03 2010
%F From _Amiram Eldar_, Jan 16 2021: (Start)
%F Sum_{n>=1} 1/a(n) = H(26)/26 = A001008(26)/A102928(26) = 34395742267/232016584800, where H(k) is the k-th harmonic number.
%F Sum_{n>=1} (-1)^(n+1)/a(n) = 18051406831/696049754400. (End)
%F From _G. C. Greubel_, Mar 13 2022: (Start)
%F G.f.: x*(27 - 25*x)/(1-x)^3.
%F E.g.f.: x*(27 + x)*exp(x). (End)
%t Table[n(n+26),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,27,56},50] (* _Harvey P. Dale_, Dec 15 2018 *)
%o (PARI) a(n)=n*(n+26) \\ _Charles R Greathouse IV_, Jun 17 2017
%o (Sage) [n*(n+26) for n in (0..50)] # _G. C. Greubel_, Mar 13 2022
%Y Cf. A001008, A002378, A005563, A028347, A028552, A028557, A028560, A028563, A028566, A028569.
%Y Cf. A098849, A098850, A098603, A098847, A098848, A102928, A120071, A132759, A132760, A132761.
%Y Cf. A132762, A132763, A132764, A132765, A132766, A132767.
%K nonn,easy
%O 0,2
%A _Omar E. Pol_, Aug 28 2007