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%I #25 Sep 08 2022 08:45:41
%S 2024,8098,18222,32396,50620,72894,99218,129592,164016,202490,245014,
%T 291588,342212,396886,455610,518384,585208,656082,731006,809980,
%U 893004,980078,1071202,1166376,1265600,1368874,1476198,1587572,1702996,1822470
%N a(n) = 2025*n^2 - n.
%C The identity (32805000*n^2 - 16200*n+1)^2 - (2025*n^2 - n)*(729000*n - 180)^2 = 1 can be written as A157080(n)^2 - a(n)*A156867(n)^2 = 1.
%H Vincenzo Librandi, <a href="/A156855/b156855.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*(2024+2026*x)/(1-x)^3.
%F E.g.f.: x*(2024 + 2025*x)*exp(x). - _G. C. Greubel_, Jan 28 2022
%t Table[n (2025*n - 1), {n, 40}] (* _Wesley Ivan Hurt_, Oct 10 2021 *)
%o (Magma) I:=[2024, 8098, 18222]; [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)=2025*n^2-n \\ _Charles R Greathouse IV_, Dec 23 2011
%o (Sage) [n*(2025*n -1) for n in (1..40)] # _G. C. Greubel_, Jan 28 2022
%Y Cf. A156856, A156867, A157080.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Feb 17 2009; corrected Feb 20 2009
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