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A120071 a(n) = n*(n+20). 18

%I

%S 0,21,44,69,96,125,156,189,224,261,300,341,384,429,476,525,576,629,

%T 684,741,800,861,924,989,1056,1125,1196,1269,1344,1421,1500,1581,1664,

%U 1749,1836,1925,2016,2109,2204,2301

%N a(n) = n*(n+20).

%D F. P. Muga II, Extending the Golden Ratio and the Binet-de Moivre Formula, March 2014; Preprint on ResearchGate.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F a(n) = (n+10)^2 - 10^2 = n*(n+20), n>=0.

%F G.f.: x*(21-19*x)/(1-x)^3.

%F a(n) = 2*n + a(n-1) + 19 (with a(0)=0). - _Vincenzo Librandi_, Nov 13 2010

%p seq(sum(4*k-n, k=7..n), n=6..51); # _Zerinvary Lajos_, Feb 17 2008

%t s=0;lst={};Do[s+=n;AppendTo[lst,s],{n,21,6!,2}];lst (* _Vladimir Joseph Stephan Orlovsky_, Feb 26 2009 *)

%o (PARI) a(n)=n*(n+20) \\ _Charles R Greathouse IV_, Jan 21 2015

%Y a(n-10), n>=11, tenth column (used for the n=10 series of the hydrogen atom) of triangle A120070.

%Y For n*(n+18) see A098850.

%Y Cf. A001477, A098849, A120061, A132765, A132760, A132761, A132762, A005563, A028552, A028347, A028557, A028560, A028563, A028566, A028569, A098603, A098847, A132759, A098848.

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Jul 20 2006

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Last modified March 26 22:42 EDT 2019. Contains 321565 sequences. (Running on oeis4.)