%I #30 Aug 23 2018 02:22:42
%S 0,13,32,57,88,125,168,217,272,333,400,473,552,637,728,825,928,1037,
%T 1152,1273,1400,1533,1672,1817,1968,2125,2288,2457,2632,2813,3000,
%U 3193,3392,3597,3808,4025,4248,4477,4712,4953,5200,5453,5712
%N a(n) = n*(3*n + 10).
%H Harvey P. Dale, <a href="/A140678/b140678.txt">Table of n, a(n) for n = 0..1000</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 + 10*n.
%F a(n) = 6*n + a(n-1) + 7, with a(0)=0. - _Vincenzo Librandi_, Aug 03 2010
%F G.f.: x*(13 - 7*x)/(1 - x)^3. - _Arkadiusz Wesolowski_, Dec 24 2011
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3), with a(0)=0, a(1)=13, a(2)=32. - _Harvey P. Dale_, Jun 05 2012
%F E.g.f.: (3*x^2 + 13*x)*exp(x). - _G. C. Greubel_, Jul 20 2017
%t Table[n (3 n + 10), {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 13, 32}, 50] (* _Harvey P. Dale_, Jun 05 2012 *)
%o (PARI) a(n)=n*(3*n+10) \\ _Charles R Greathouse IV_, Oct 07 2015
%Y Cf. A033428, A045944, A140676, A067725, A140677, A067707, A140679, A140680, A140681, A140689.
%K nonn,easy
%O 0,2
%A _Omar E. Pol_, May 22 2008