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%I #26 Sep 08 2022 08:45:41
%S 44,70,546,1472,2848,4674,6950,9676,12852,16478,20554,25080,30056,
%T 35482,41358,47684,54460,61686,69362,77488,86064,95090,104566,114492,
%U 124868,135694,146970,158696,170872,183498,196574,210100,224076,238502,253378
%N a(n) = 225*n^2 - 199*n + 44.
%H Vincenzo Librandi, <a href="/A156812/b156812.txt">Table of n, a(n) for n = 0..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 - 199)^2.
%F G.f.: (44 - 62*x + 468*x^2)/(1-x)^3.
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
%F E.g.f.: (44 + 26*x + 225*x^2)*exp(x). - _G. C. Greubel_, Jun 10 2021
%t LinearRecurrence[{3,-3,1}, {44,70,546}, 40] (* _Vincenzo Librandi_, Feb 08 2012 *)
%o (PARI) a(n)=225*n^2-199*n+44 \\ _Charles R Greathouse IV_, Dec 23 2011
%o (Magma) I:=[44, 70, 546]; [n le 3 select I[n] else 3*Self(n-1) -3*Self(n-2) +Self(n-3): n in [1..40]]; // _Vincenzo Librandi_, Feb 08 2012
%o (Sage) [225*n^2 -199*n +44 for n in (0..40)] # _G. C. Greubel_, Jun 10 2021
%Y Cf. A156813, A156814.
%K nonn,easy
%O 0,1
%A _Vincenzo Librandi_, Feb 16 2009
%E Offset corrected by _R. J. Mathar_, Aug 18 2009
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