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a(n) = n*(3*n+14).
7

%I #19 Jul 21 2017 02:03:15

%S 0,17,40,69,104,145,192,245,304,369,440,517,600,689,784,885,992,1105,

%T 1224,1349,1480,1617,1760,1909,2064,2225,2392,2565,2744,2929,3120,

%U 3317,3520,3729,3944,4165,4392,4625,4864,5109,5360,5617

%N a(n) = n*(3*n+14).

%H G. C. Greubel, <a href="/A140679/b140679.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 + 14*n.

%F a(n) = a(n-1) + 6*n + 11, with a(0)=0. - _Vincenzo Librandi_, Aug 03 2010

%F a(n) = 3a(n-1) - 3a(n-2) + a(n-3), with a(1)=0, a(2)=17, a(3)=40. - Harvey P. Dale, Apr 29 2011

%F E.g.f.: (3*x^2 + 17*x)*exp(x). - _G. C. Greubel_, Jul 20 2017

%e a(1)=6*1+0+11=17; a(2)=6*2+17+11=40; a(3)=6*3+40+11=69. See 2nd formula.

%t Table[n(3n+14),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,17,40},50] (* _Harvey P. Dale_, Apr 29 2011 *)

%o (PARI) a(n)=n*(3*n+14) \\ _Charles R Greathouse IV_, Oct 07 2015

%Y Cf. A033428, A045944, A140676, A067725, A140677, A140678, A067707, A140680, A140681, A140689.

%K easy,nonn

%O 0,2

%A _Omar E. Pol_, May 22 2008