A090337 Let b(0) = 1, b(n) = b(n-1) + (-1)^(n-1)*b(n-1)/10; sequence gives numerator of b(n).

1, 11, 99, 1089, 9801, 107811, 970299, 10673289, 96059601, 1056655611, 9509900499, 104608905489, 941480149401, 10356281643411, 93206534790699, 1025271882697689, 9227446944279201, 101501916387071211, 913517247483640899, 10048689722320049889

Offset

0,2

Links

Table of n, a(n) for n=0..19.

Index entries for linear recurrences with constant coefficients, signature (0,99).

Formula

From Philippe Deléham, Jan 28 2004: (Start)

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

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

Example

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

Maple

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;

Mathematica

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 *)

Crossrefs

Sequence in context: A037510 A037693 A098611 * A287196 A288362 A287953

Adjacent sequences: A090334 A090335 A090336 * A090338 A090339 A090340

Keyword

nonn,frac,easy,changed

Author

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

Extensions

Index corrected to 0, remove erroneous formula. - Ray Chandler, Oct 19 2024

Status

approved