A090337 - OEIS

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

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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

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