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

1,2

Links

Table of n, a(n) for n=1..20.

Formula

a(n) = 99^(n/2) if n is even else 11*99^((n-1)/2). a(n) = 99*a(n-2). G.f.: (1+11*x)/(1-99*x^2). - Philippe Deléham, Jan 28 2004

a(2n) = a(2n-1)*11 = 11*99^(n-1) . a(2n+1)= a(2n)*9 = 99^n . G.f.: x*(1+11x)/(1-99*x^2) . - Philippe Deléham, Jan 28 2004

a(n)=-(5/33)*(-1)^n*99^[(1/4)*(-1)^n]*99^(1/2)*n*11979^(1/4)+(2/11)*99^[(1/4)*(-1)^n]*99^(1/2 )*n*11979^(1/4), with n>=0 [From Paolo P. Lava, Nov 20 2008]

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;

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

Status

approved