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a(n) = n*(3*n + 8).
9

%I #31 Jul 21 2017 04:27:25

%S 0,11,28,51,80,115,156,203,256,315,380,451,528,611,700,795,896,1003,

%T 1116,1235,1360,1491,1628,1771,1920,2075,2236,2403,2576,2755,2940,

%U 3131,3328,3531,3740,3955,4176,4403,4636,4875,5120,5371,5628

%N a(n) = n*(3*n + 8).

%H G. C. Greubel, <a href="/A140677/b140677.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 + 8*n.

%F a(n) = 6*n + a(n-1) + 5, with a(0)=0. - _Vincenzo Librandi_, Aug 03 2010

%F G.f.: x*(11 - 5*x)/(1 - x)^3. - _Arkadiusz Wesolowski_, Dec 24 2011

%F E.g.f.: (3*x^2 + 11*x)*exp(x). - _G. C. Greubel_, Jul 20 2017

%e a(1) = 6*1 + 0 + 5 = 11; a(2) = 6*2 + 11 + 5 = 28; a(3) = 6*3 + 28 + 5 = 51. - _Vincenzo Librandi_, Aug 03 2010

%t Table[n(3n+8),{n,0,45}] (* _Harvey P. Dale_, Feb 20 2011 *)

%o (PARI) a(n)=n*(3*n+8) \\ _Charles R Greathouse IV_, Jun 17 2017

%Y Cf. A033428, A045944, A140676, A067725, A140678, A067707, A140679, A140680, A140681, A140689.

%K easy,nonn

%O 0,2

%A _Omar E. Pol_, May 22 2008