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%I #30 Sep 08 2022 08:45:41
%S 224,898,2022,3596,5620,8094,11018,14392,18216,22490,27214,32388,
%T 38012,44086,50610,57584,65008,72882,81206,89980,99204,108878,119002,
%U 129576,140600,152074,163998,176372,189196,202470,216194,230368,244992,260066
%N a(n) = 225*n^2 - n.
%H Vincenzo Librandi, <a href="/A156813/b156813.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F From _Vincenzo Librandi_, Feb 08 2012: (Start)
%F 900*a(n) + 1 = (450*n - 1)^2.
%F G.f.: 2*x*(112 + 113*x)/(1-x)^3.
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
%F E.g.f.: x*(224 + 225*x)*exp(x). - _G. C. Greubel_, Jun 10 2021
%t LinearRecurrence[{3, -3, 1}, {224, 898, 2022}, 50] (* _Vincenzo Librandi_, Feb 08 2012 *)
%o (PARI) a(n)=225*n^2-n \\ _Charles R Greathouse IV_, Dec 23 2011
%o (Magma) I:=[224, 898, 2022]; [n le 3 select I[n] else 3*Self(n-1) -3*Self(n-2) +Self(n-3): n in [1..50]]; // _Vincenzo Librandi_, Feb 08 2012
%o (Sage) [n*(225*n -1) for n in (1..50)] # _G. C. Greubel_, Jun 10 2021
%Y Cf. A156814.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Feb 16 2009
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