|
%I #22 Sep 08 2022 08:45:41
%S 198,927,1656,2385,3114,3843,4572,5301,6030,6759,7488,8217,8946,9675,
%T 10404,11133,11862,12591,13320,14049,14778,15507,16236,16965,17694,
%U 18423,19152,19881,20610,21339,22068,22797,23526,24255,24984,25713
%N a(n) = 729*n - 531.
%C The identity (6561*n^2 - 9558*n + 3482)^2 - (81*n^2 - 118*n + 43)*(729*n - 531)^2 = 1 can be written as A156773(n)^2 - A156677(n)*a(n)^2 = 1.
%H Vincenzo Librandi, <a href="/A156771/b156771.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*(198 + 531*x)/(1-x)^2.
%F E.g.f.: 9*(59 - (59 - 81*x)*exp(x)). - _G. C. Greubel_, Jun 19 2021
%t LinearRecurrence[{2,-1},{198,927},40]
%o (Magma) I:=[198, 927]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
%o (PARI) a(n)=729*n-531 \\ _Charles R Greathouse IV_, Dec 23 2011
%o (Sage) [9*(81*n -59) for n in [1..50]] # _G. C. Greubel_, Jun 19 2021
%Y Cf. A156677, A156773.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Feb 15 2009
|
