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%I #30 Sep 08 2022 08:45:41
%S 729180,1458180,2187180,2916180,3645180,4374180,5103180,5832180,
%T 6561180,7290180,8019180,8748180,9477180,10206180,10935180,11664180,
%U 12393180,13122180,13851180,14580180,15309180,16038180,16767180,17496180
%N a(n) = 729000*n + 180.
%C The identity (32805000*n^2 + 16200*n + 1)^2 - (2025*n^2 + n)*(729000*n + 180)^2 = 1 can be written as A157081(n)^2 - A156856(n)*a(n)^2 = 1.
%H Vincenzo Librandi, <a href="/A156868/b156868.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F a(n) = 2*a(n-1) - a(n-2).
%F G.f.: 180*x*(4051-x)/(1-x)^2.
%F E.g.f.: 180*(-1 + (1 + 4050*x)*exp(x)). - _G. C. Greubel_, Jan 28 2022
%t LinearRecurrence[{2,-1},{729180,1458180},40]
%t 729000*Range[30]+180 (* _Harvey P. Dale_, Jan 11 2014 *)
%o (Magma) I:=[729180, 1458180]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..30]];
%o (PARI) a(n)=729000*n+180 \\ _Charles R Greathouse IV_, Dec 23 2011
%o (Sage) [180*(4050*n + 1) for n in (1..40)] # _G. C. Greubel_, Jan 28 2022
%Y Cf. A156856, A156867, A157081.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Feb 17 2009
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