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A090337
Let b(0) = 1, b(n) = b(n-1) + (-1)^(n-1)*b(n-1)/10; sequence gives numerator of b(n).
0
1, 11, 99, 1089, 9801, 107811, 970299, 10673289, 96059601, 1056655611, 9509900499, 104608905489, 941480149401, 10356281643411, 93206534790699, 1025271882697689, 9227446944279201, 101501916387071211, 913517247483640899, 10048689722320049889
OFFSET
0,2
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
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