cp's OEIS Frontend

A132765 a(n) = n*(n + 23).

%I A132765 #39 Mar 14 2022 02:45:05
%S A132765 0,24,50,78,108,140,174,210,248,288,330,374,420,468,518,570,624,680,
%T A132765 738,798,860,924,990,1058,1128,1200,1274,1350,1428,1508,1590,1674,
%U A132765 1760,1848,1938,2030,2124,2220,2318,2418,2520,2624,2730,2838,2948,3060,3174,3290,3408
%N A132765 a(n) = n*(n + 23).
%H A132765 G. C. Greubel, <a href="/A132765/b132765.txt">Table of n, a(n) for n = 0..5000</a>
%H A132765 Felix P. Muga II, <a href="https://www.researchgate.net/publication/267327689">Extending the Golden Ratio and the Binet-de Moivre Formula</a>, ResearchGate, 2014.
%H A132765 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A132765 a(n) = n*(n + 23).
%F A132765 a(n) = 2*n + a(n-1) + 22 for n>0, a(0)=0. - _Vincenzo Librandi_, Aug 03 2010
%F A132765 From _Chai Wah Wu_, Dec 17 2016: (Start)
%F A132765 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2.
%F A132765 G.f.: 2*x*(12 - 11*x)/(1-x)^3. (End)
%F A132765 From _Amiram Eldar_, Jan 16 2021: (Start)
%F A132765 Sum_{n>=1} 1/a(n) = H(23)/23 = A001008(23)/A102928(23) = 444316699/2736605872, where H(k) is the k-th harmonic number.
%F A132765 Sum_{n>=1} (-1)^(n+1)/a(n) = 2*log(2)/23 - 3825136961/123147264240. (End)
%F A132765 E.g.f.: x*(24 + x)*exp(x). - _G. C. Greubel_, Mar 14 2022
%t A132765 Table[n (n + 23), {n, 0, 50}] (* _Bruno Berselli_, Sep 03 2018 *)
%o A132765 (PARI) a(n)=n*(n+23) \\ _Charles R Greathouse IV_, Jun 17 2017
%o A132765 (Sage) [n*(n+23) for n in (0..50)] # _G. C. Greubel_, Mar 14 2022
%Y A132765 Cf. A001008, A001477, A002378, A005563, A028347, A028552, A028557, A028560, A028563, A028566, A028569, A056126, A098603, A098847, A098848, A098849, A098850, A102928, A120071, A132759, A132760, A132761, A132762, A132763, A132764, A132765, A132766.
%K A132765 nonn,easy
%O A132765 0,2
%A A132765 _Omar E. Pol_, Aug 28 2007