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A132766 a(n) = n*(n+24).

%I A132766 #28 Mar 14 2022 02:45:09
%S A132766 0,25,52,81,112,145,180,217,256,297,340,385,432,481,532,585,640,697,
%T A132766 756,817,880,945,1012,1081,1152,1225,1300,1377,1456,1537,1620,1705,
%U A132766 1792,1881,1972,2065,2160,2257,2356,2457,2560,2665,2772,2881,2992,3105,3220,3337
%N A132766 a(n) = n*(n+24).
%H A132766 G. C. Greubel, <a href="/A132766/b132766.txt">Table of n, a(n) for n = 0..5000</a>
%H A132766 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 A132766 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A132766 a(n) = n*(n + 24).
%F A132766 a(n) = 2*n + a(n-1) + 23 (with a(0)=0). - _Vincenzo Librandi_, Aug 03 2010
%F A132766 a(0)=0, a(1)=25, a(2)=52; for n>2, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Harvey P. Dale_, Feb 11 2016
%F A132766 From _Amiram Eldar_, Jan 16 2021: (Start)
%F A132766 Sum_{n>=1} 1/a(n) = H(24)/24 = A001008(24)/A102928(24) = 1347822955/8566766208, where H(k) is the k-th harmonic number.
%F A132766 Sum_{n>=1} (-1)^(n+1)/a(n) = 3602044091/128501493120. (End)
%F A132766 From _G. C. Greubel_, Mar 14 2022: (Start)
%F A132766 G.f.: 2*x*(13 - 12*x)/(1-x)^3.
%F A132766 E.g.f.: x*(26 + x)*exp(x). (End)
%t A132766 Table[n (n + 24), {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 25, 52}, 50] (* _Harvey P. Dale_, Feb 11 2016 *)
%o A132766 (PARI) a(n)=n*(n+24) \\ _Charles R Greathouse IV_, Jun 17 2017
%o A132766 (Sage) [n*(n+24) for n in (0..50)] # _G. C. Greubel_, Mar 14 2022
%Y A132766 Cf. A001008, A002378, A005563, A028347, A028552, A028557, A028560, A028563, A028566, A028569, A098603, A098849, A098850, A098847, A098848, A102928, A120071, A132759, A132760, A132761, A132762, A132763, A132764, A132765.
%K A132766 easy,nonn
%O A132766 0,2
%A A132766 _Omar E. Pol_, Aug 28 2007