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%I #21 Nov 29 2024 20:28:24
%S 0,21,46,75,108,145,186,231,280,333,390,451,516,585,658,735,816,901,
%T 990,1083,1180,1281,1386,1495,1608,1725,1846,1971,2100,2233,2370,2511,
%U 2656,2805,2958,3115,3276,3441,3610,3783,3960,4141
%N a(n) = n*(2*n + 19).
%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 + 19*n.
%F a(n) = a(n-1) + 4*n + 17 (with a(0)=0). - _Vincenzo Librandi_, Nov 24 2010
%F From _Elmo R. Oliveira_, Nov 29 2024: (Start)
%F G.f.: x*(21 - 17*x)/(1-x)^3.
%F E.g.f.: exp(x)*x*(21 + 2*x).
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
%t Table[n(2n+19),{n,0,50}] (* _Harvey P. Dale_, Jan 26 2011 *)
%o (PARI) a(n)=n*(2*n+19) \\ _Charles R Greathouse IV_, Jun 17 2017
%Y Cf. A014105, A014106, A033537, A130861, A139576, A139577, A139578, A139579, A139580.
%K easy,nonn
%O 0,2
%A _Omar E. Pol_, May 19 2008