cp's OEIS Frontend

A132773 a(n) = n*(n + 31).

%I A132773 #35 Dec 14 2024 07:19:24
%S A132773 0,32,66,102,140,180,222,266,312,360,410,462,516,572,630,690,752,816,
%T A132773 882,950,1020,1092,1166,1242,1320,1400,1482,1566,1652,1740,1830,1922,
%U A132773 2016,2112,2210,2310,2412,2516,2622,2730,2840,2952,3066,3182,3300,3420,3542,3666
%N A132773 a(n) = n*(n + 31).
%H A132773 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 A132773 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A132773 G.f.: 2*x*(-16+15*x)/(-1+x)^3. - _R. J. Mathar_, Nov 14 2007
%F A132773 a(n) = 2*A132758(n). - _R. J. Mathar_, Jul 22 2009
%F A132773 a(n) = 2*n + a(n-1) + 30, with n > 0, a(0)=0. - _Vincenzo Librandi_, Aug 03 2010
%F A132773 From _Amiram Eldar_, Jan 16 2021: (Start)
%F A132773 Sum_{n>=1} 1/a(n) = H(31)/31 = A001008(31)/A102928(31) = 290774257297357/2238255069850800, where H(k) is the k-th harmonic number.
%F A132773 Sum_{n>=1} (-1)^(n+1)/a(n) = 2*log(2)/31 - 7313175618421/319750724264400. (End)
%F A132773 From _Elmo R. Oliveira_, Dec 13 2024: (Start)
%F A132773 E.g.f.: exp(x)*x*(32 + x).
%F A132773 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
%t A132773 Table[n*(n + 31), {n, 0, 100}] (* _Wesley Ivan Hurt_, Apr 16 2024 *)
%o A132773 (PARI) a(n)=n*(n+31) \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A132773 Cf. A001008, A002378, A005563, A028347, A028552, A028557, A028560, A028563, A028566, A028569.
%Y A132773 Cf. A098603, A098847, A098848, A098849, A098850, A102928, A120071, A132758, A132759, A132760.
%Y A132773 Cf. A132761, A132762, A132763, A132764, A132765, A132766, A132767, A132768, A132769, A132770.
%Y A132773 Cf. A132771, A132772.
%K A132773 nonn,easy
%O A132773 0,2
%A A132773 _Omar E. Pol_, Aug 28 2007