A168522 a(n) = 98*a(n-1) - 2*a(n-2); a(1) = 0, a(2) = 1.

0, 1, 98, 9602, 940800, 92179196, 9031679608, 884920243192, 86704120473600, 8495233965926416, 832359520419841568, 81554242533212620832, 7990651049213997158400, 782920694337905296281536, 76710246743016291041273728, 7516038339426920711452262272

Offset: 1

Author

Mark Dols, Nov 28 2009

Keywords

• nonn
• easy

Comments

a(n)/a(n+1) converges to 49 - sqrt(2399). - corrected by Mark Dols, Jun 20 2010

Links

• G. C. Greubel, Table of n, a(n) for n = 1..200
• Index entries for linear recurrences with constant coefficients, signature (98,-2).

Crossrefs

Cf. A168520, A004189, A000108, A000984, A165293

Programs

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

Mathematica

LinearRecurrence[{98,-2},{0,1}, 25] (* G. C. Greubel, Jul 25 2016 *)

Formula

G.f.: x^2/(1 - 98x + 2x^2). - Philippe Deléham, Nov 29 2009

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

Extensions

Definition adapted to offset by Georg Fischer, Jun 19 2021