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a(n) = n*(3*n+16).
7

%I #20 Aug 23 2020 14:15:35

%S 0,19,44,75,112,155,204,259,320,387,460,539,624,715,812,915,1024,1139,

%T 1260,1387,1520,1659,1804,1955,2112,2275,2444,2619,2800,2987,3180,

%U 3379,3584,3795,4012,4235,4464,4699,4940,5187,5440,5699

%N a(n) = n*(3*n+16).

%H G. C. Greubel, <a href="/A140680/b140680.txt">Table of n, a(n) for n = 0..5000</a>

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

%F a(n) = 3*n^2 + 16*n.

%F a(n) = 6*n + a(n-1) + 13 (with a(0)=0). - _Vincenzo Librandi_, Aug 03 2010

%F E.g.f.: (3*x^2 + 19*x)*exp(x). - _G. C. Greubel_, Jul 20 2017

%t a[n_]:=Sum[6*i+13, {i, 1, n}]; (* _Vladimir Joseph Stephan Orlovsky_, Dec 04 2008 *)

%t Table[n(3n+16),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,19,44},50] (* _Harvey P. Dale_, Aug 23 2020 *)

%o (PARI) a(n)=n*(3*n+16) \\ _Charles R Greathouse IV_, Jun 17 2017

%Y Cf. A033428, A045944, A140676, A067725, A140677, A140678, A067707, A140679, A140681, A140689.

%K nonn,easy

%O 0,2

%A _Omar E. Pol_, May 22 2008