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%I #24 Sep 08 2022 08:45:41
%S 226,902,2028,3604,5630,8106,11032,14408,18234,22510,27236,32412,
%T 38038,44114,50640,57616,65042,72918,81244,90020,99246,108922,119048,
%U 129624,140650,152126,164052,176428,189254,202530,216256,230432,245058,260134
%N a(n) = 225*n^2 + n.
%H Vincenzo Librandi, <a href="/A156814/b156814.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*(113 + 112*x)/(1-x)^3.
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
%F E.g.f.: x*(226 + 225*x)*exp(x). - _G. C. Greubel_, Jun 10 2021
%t LinearRecurrence[{3, -3, 1}, {226, 902, 2028}, 50] (* _Vincenzo Librandi_, Feb 08 2012 *)
%o (PARI) a(n)=225*n^2+n \\ _Charles R Greathouse IV_, Dec 23 2011
%o (Magma) I:=[226, 902, 2028]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // _Vincenzo Librandi_, Feb 08 2012
%o (Sage) [n*(1+225*n) for n in [1..50]] # _G. C. Greubel_, Jun 10 2021
%Y Cf. A156840.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Feb 16 2009
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