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a(n) = 98*a(n-1) - 2*a(n-2); a(1) = 0, a(2) = 1.
2

%I #28 Jan 03 2024 08:51:06

%S 0,1,98,9602,940800,92179196,9031679608,884920243192,86704120473600,

%T 8495233965926416,832359520419841568,81554242533212620832,

%U 7990651049213997158400,782920694337905296281536,76710246743016291041273728,7516038339426920711452262272

%N a(n) = 98*a(n-1) - 2*a(n-2); a(1) = 0, a(2) = 1.

%C a(n)/a(n+1) converges to 49 - sqrt(2399). - corrected by _Mark Dols_, Jun 20 2010

%H G. C. Greubel, <a href="/A168522/b168522.txt">Table of n, a(n) for n = 1..200</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (98,-2).

%F G.f.: x^2/(1 - 98x + 2x^2). - _Philippe Deléham_, Nov 29 2009

%F E.g.f.: (1/(2*b))*exp(49*x)*( 49*sinh(b*x) - b*cosh(b*x) ) - (1/2), where b = sqrt(2399). - _G. C. Greubel_, Jul 25 2016

%t LinearRecurrence[{98,-2},{0,1}, 25] (* _G. C. Greubel_, Jul 25 2016 *)

%o (Magma) [n le 2 select n-1 else 98*Self(n-1)-2*Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, Jul 25 2016

%Y Cf. A168520, A004189, A000108, A000984, A165293

%K nonn,easy

%O 1,3

%A _Mark Dols_, Nov 28 2009

%E Definition adapted to offset by _Georg Fischer_, Jun 19 2021