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A090337
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Let b(0) = 1, b(n) = b(n-1) + (-1)^(n-1)*b(n-1)/10; sequence gives numerator of b(n).
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0
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1, 11, 99, 1089, 9801, 107811, 970299, 10673289, 96059601, 1056655611, 9509900499, 104608905489, 941480149401, 10356281643411, 93206534790699, 1025271882697689, 9227446944279201, 101501916387071211, 913517247483640899, 10048689722320049889
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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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). - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), 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) . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), 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 (paoloplava(AT)gmail.com), Nov 20 2008]
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EXAMPLE
| 1, 11/10, 99/100, 1089/1000, 9801/10000, 107811/100000, 970299/1000000, ...
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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;
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CROSSREFS
| Sequence in context: A037510 A037693 A098611 * A066329 A001738 A120655
Adjacent sequences: A090334 A090335 A090336 * A090338 A090339 A090340
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KEYWORD
| nonn,frac
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AUTHOR
| Dario Ramos (dario_metal(AT)hotmail.com), Jan 27 2004
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