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A132770 a(n) = n*(n + 28).

%I A132770 #33 Mar 13 2022 05:50:40
%S A132770 0,29,60,93,128,165,204,245,288,333,380,429,480,533,588,645,704,765,
%T A132770 828,893,960,1029,1100,1173,1248,1325,1404,1485,1568,1653,1740,1829,
%U A132770 1920,2013,2108,2205,2304,2405,2508,2613,2720,2829,2940,3053,3168,3285,3404,3525
%N A132770 a(n) = n*(n + 28).
%H A132770 G. C. Greubel, <a href="/A132770/b132770.txt">Table of n, a(n) for n = 0..5000</a>
%H A132770 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 A132770 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A132770 a(n) = 2*n + a(n-1) + 27, with a(0)=0. - _Vincenzo Librandi_, Aug 03 2010
%F A132770 From _Amiram Eldar_, Jan 16 2021: (Start)
%F A132770 Sum_{n>=1} 1/a(n) = H(28)/28 = A001008(28)/A102928(28) = 315404588903/2248776129600, where H(k) is the k-th harmonic number.
%F A132770 Sum_{n>=1} (-1)^(n+1)/a(n) = 7751493599/321253732800. (End)
%F A132770 G.f.: x*(29 - 27*x)/(1-x)^3. - _Harvey P. Dale_, Aug 03 2021
%F A132770 E.g.f.: x*(29 + x)*exp(x). - _G. C. Greubel_, Mar 13 2022
%t A132770 #(#+28)&/@Range[0,50] (* or *) LinearRecurrence[{3,-3,1},{0,29,60},50] (* _Harvey P. Dale_, Apr 30 2018 *)
%o A132770 (PARI) a(n)=n*(n+28) \\ _Charles R Greathouse IV_, Jun 17 2017
%o A132770 (Sage) [n*(n+28) for n in (0..50)] # _G. C. Greubel_, Mar 13 2022
%Y A132770 Cf. A001008, A002378, A005563, A028347, A028552, A028557, A028560, A028563, A028566, A028569.
%Y A132770 Cf. A098603, A098847, A098848, A098849, A098850, A102928, A120071, A132759, A132760, A132761.
%Y A132770 Cf. A132762, A132763, A132764, A132765, A132766, A132767, A132768, A132769.
%K A132770 nonn,easy
%O A132770 0,2
%A A132770 _Omar E. Pol_, Aug 28 2007