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%I #38 Mar 13 2022 03:31:08
%S 0,31,64,99,136,175,216,259,304,351,400,451,504,559,616,675,736,799,
%T 864,931,1000,1071,1144,1219,1296,1375,1456,1539,1624,1711,1800,1891,
%U 1984,2079,2176,2275,2376,2479,2584,2691,2800,2911,3024,3139,3256,3375,3496,3619
%N a(n) = n*(n + 30).
%H Harvey P. Dale, <a href="/A132772/b132772.txt">Table of n, a(n) for n = 0..1000</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 G.f.: x*(31-29*x)/(1-x)^3. - _R. J. Mathar_, Nov 14 2007
%F a(n) = 2*n + a(n-1) + 29 (with a(0)=0). - _Vincenzo Librandi_, Aug 03 2010
%F a(0)=0, a(1)=31, a(2)=64, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Harvey P. Dale_, Mar 06 2015
%F From _Amiram Eldar_, Jan 16 2021: (Start)
%F Sum_{n>=1} 1/a(n) = H(30)/30 = A001008(30)/A102928(30) = 9304682830147/69872686884000, where H(k) is the k-th harmonic number.
%F Sum_{n>=1} (-1)^(n+1)/a(n) = 225175759291/9981812412000. (End)
%F E.g.f.: x*(31 + x)*exp(x). - _G. C. Greubel_, Mar 13 2022
%t Table[n(n+30),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,31,64},50] (* _Harvey P. Dale_, Mar 06 2015 *)
%o (PARI) a(n)=n*(n+30) \\ _Charles R Greathouse IV_, Jun 17 2017
%o (Sage) [n*(n+30) for n in (0..50)] # _G. C. Greubel_, Mar 13 2022
%Y Cf. A001008, A002378, A005563, A028347, A028552, A028557, A028560, A028563, A028566.
%Y Cf. A028569, A067079, A098849, A098850, A098603, A098847, A098848, A102928, A120071.
%Y Cf. A132759, A132760, A132761, A132762, A132763, A132764, A132765, A132766, A132767.
%Y Cf. A132768, A132769, A132770, A132771.
%K nonn,easy
%O 0,2
%A _Omar E. Pol_, Aug 28 2007
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