%I #18 Oct 19 2024 11:52:21

%S 1,11,99,1089,9801,107811,970299,10673289,96059601,1056655611,

%T 9509900499,104608905489,941480149401,10356281643411,93206534790699,

%U 1025271882697689,9227446944279201,101501916387071211,913517247483640899,10048689722320049889

%N Let b(0) = 1, b(n) = b(n-1) + (-1)^(n-1)*b(n-1)/10; sequence gives numerator of b(n).

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,99).

%F From _Philippe Deléham_, Jan 28 2004: (Start)

%F a(0) = 1, a(1) = 11, a(n) = 99*a(n-2) for n > 1.

%F G.f.: (1+11*x)/(1-99*x^2). (End

%e 1, 11/10, 99/100, 1089/1000, 9801/10000, 107811/100000, 970299/1000000, ...

%p b := proc(n) option remember; if n = 0 then 1 else expand(simplify(b(n-1)+(-1)^(n+1)*b(n-1)/10)); fi; end;

%t nxt[{n_,a_}]:={n+1,Numerator[a+(a (-1)^n)/10]}; NestList[nxt,{0,1},20][[;;,2]] (* or *) LinearRecurrence[{0,99},{1,11},20] (* _Harvey P. Dale_, Oct 18 2024 *)

%K nonn,frac

%O 0,2

%A Dario Ramos (dario_metal(AT)hotmail.com), Jan 27 2004

%E Index corrected to 0, remove erroneous formula. - _Ray Chandler_, Oct 19 2024