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%I #22 Sep 08 2022 08:45:41
%S 531,1260,1989,2718,3447,4176,4905,5634,6363,7092,7821,8550,9279,
%T 10008,10737,11466,12195,12924,13653,14382,15111,15840,16569,17298,
%U 18027,18756,19485,20214,20943,21672,22401,23130,23859,24588,25317,26046
%N a(n) = 729*n - 198.
%C The identity (6561*n^2 - 3564*n + 485)^2 - (81*n^2 - 44*n + 6)*(729*n - 198)^2 = 1 can be written as A156774(n)^2 - A156676(n)*a(n)^2 = 1.
%H Vincenzo Librandi, <a href="/A156772/b156772.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.: x*(531 + 198*x)/(1-x)^2.
%F E.g.f.: 9*(22 - (22 - 81*x)*exp(x)). - _G. C. Greubel_, Jun 19 2021
%t LinearRecurrence[{2,-1}, {531,1260}, 40]
%o (Magma) I:=[531, 1260]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
%o (PARI) a(n)=729*n-198 \\ _Charles R Greathouse IV_, Dec 23 2011
%o (Sage) [9*(81*n -22) for n in [1..50]] # _G. C. Greubel_, Jun 19 2021
%Y Cf. A156676, A156774.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Feb 15 2009
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