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a(n) = n*(2*n + 11).
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%I #24 Nov 29 2024 20:19:42

%S 0,13,30,51,76,105,138,175,216,261,310,363,420,481,546,615,688,765,

%T 846,931,1020,1113,1210,1311,1416,1525,1638,1755,1876,2001,2130,2263,

%U 2400,2541,2686,2835,2988,3145,3306,3471,3640,3813,3990

%N a(n) = n*(2*n + 11).

%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 + 11*n.

%F a(n) = a(n-1) + 4*n + 9 (with a(0)=0). - _Vincenzo Librandi_, Nov 24 2010

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

%F G.f.: x*(13 - 9*x)/(1-x)^3.

%F E.g.f.: exp(x)*x*(13 + 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++ +13;AppendTo[lst, s], {n, 0, 7!, 4}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 19 2008 *)

%t Table[n(2n+11),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,13,30},50] (* _Harvey P. Dale_, Mar 17 2019 *)

%o (PARI) a(n)=n*(2*n+11) \\ _Charles R Greathouse IV_, Jun 17 2017

%Y Cf. A014105, A014106, A033537, A130861, A139576, A139578, A139579, A139580, A139581.

%K easy,nonn

%O 0,2

%A _Omar E. Pol_, May 19 2008