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a(n) = n*(2*n + 13).
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%I #22 Nov 29 2024 20:19:55

%S 0,15,34,57,84,115,150,189,232,279,330,385,444,507,574,645,720,799,

%T 882,969,1060,1155,1254,1357,1464,1575,1690,1809,1932,2059,2190,2325,

%U 2464,2607,2754,2905,3060,3219,3382,3549,3720,3895,4074,4257,4444,4635,4830,5029

%N a(n) = n*(2*n + 13).

%H Harvey P. Dale, <a href="/A139578/b139578.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) = 2*n^2 + 13*n.

%F a(n) = a(n-1) + 4*n + 11 (with a(0)=0). - _Vincenzo Librandi_, Nov 24 2010

%F From _Elmo R. Oliveira_, Nov 29 2024: (Start)

%F G.f.: x*(15 - 11*x)/(1 - x)^3.

%F E.g.f.: exp(x)*x*(15 + 2*x).

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)

%t s=0;lst={s};Do[s+=n++ +15;AppendTo[lst, s], {n, 0, 7!, 4}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 19 2008 *)

%t Table[n(2n+13),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,15,34},50] (* _Harvey P. Dale_, Nov 22 2014 *)

%o (PARI) a(n)=n*(2*n+13) \\ _Charles R Greathouse IV_, Oct 07 2015

%Y Cf. A014105, A014106, A033537, A130861, A139576, A139577, A139579, A139580, A139581.

%K easy,nonn

%O 0,2

%A _Omar E. Pol_, May 19 2008