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%I #23 Sep 08 2022 08:45:41
%S 32821201,131252401,295293601,524944801,820206001,1181077201,
%T 1607558401,2099649601,2657350801,3280662001,3969583201,4724114401,
%U 5544255601,6430006801,7381368001,8398339201,9480920401,10629111601,11842912801
%N a(n) = 32805000*n^2 + 16200*n + 1.
%C The identity (32805000*n^2 + 16200*n + 1)^2 - (2025*n^2 + n)*(729000*n + 180)^2 = 1 can be written as a(n)^2 - A156856(n)*A156868(n)^2 = 1.
%H Vincenzo Librandi, <a href="/A157081/b157081.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*(32821201 + 32788798*x + x^2)/(1-x)^3.
%F E.g.f.: -1 + (1 + 32821200*x + 32805000*x^2)*exp(x). - _G. C. Greubel_, Jan 27 2022
%t LinearRecurrence[{3,-3,1},{32821201,131252401,295293601},40]
%o (Magma) I:=[32821201, 131252401, 295293601]; [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+16200*n+1 \\ _Charles R Greathouse IV_, Dec 23 2011
%o (Sage) [16200*n*(2025*n + 1) + 1 for n in (1..30)] # _G. C. Greubel_, Jan 27 2022
%Y Cf. A156856, A156868, A157078, A157079, A157080.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Feb 22 2009
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