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%I #27 Sep 08 2022 08:45:41
%S 23133601,111034801,264546001,483667201,768398401,1118739601,
%T 1534690801,2016252001,2563423201,3176204401,3854595601,4598596801,
%U 5408208001,6283429201,7224260401,8230701601,9302752801,10440414001,11643685201
%N a(n) = 32805000*n^2 - 10513800*n + 842401.
%C The identity (32805000*n^2 - 10513800*n + 842401)^2 - (2025*n^2 - 3401*n + 1428)*(729000*n - 116820)^2 = 1 can be written as a(n)^2 - A156854(n)*A156866(n)^2 = 1.
%H Vincenzo Librandi, <a href="/A157079/b157079.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 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
%F G.f.: x*(23133601 + 41633998*x + 842401*x^2)/(1-x)^3.
%F E.g.f.: -842401 + (842401 + 22291200*x + 32805000*x^2)*exp(x). - _G. C. Greubel_, Jan 27 2022
%t LinearRecurrence[{3,-3,1},{23133601,111034801,264546001},40]
%o (Magma) I:=[23133601, 111034801, 264546001]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];
%o (PARI) a(n)=32805000*n^2-10513800*n+842401 \\ _Charles R Greathouse IV_, Dec 23 2011
%o (Sage) [16200*n*(2025*n - 649) + 842401 for n in (1..30)] # _G. C. Greubel_, Jan 27 2022
%Y Cf. A156854, A156866, A157078, A157080, A157081.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Feb 22 2009