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Search: id:A074935
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| A074935 |
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Denominator of a(n), where for n > 2, a(n)=-1/a(n-1)+1/a(n-2), a(1)=1, a(2)=2. |
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+0
2
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| 1, 1, 2, 2, 3, 24, 200, 6675, 3045936, 46360115600, 251445391554623475, 23318100352452485482468409184
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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a(n)->-(-1)^n sqrt(2), a slowly converging sequence. In general, for recursive sequence: a(n)=Sum[i=1,...,k<n,c(i)/a(i)], asymptotic solution is: a(n)-> +/- Sqrt[Sum[i=1,..,k,abs[c(i)]]], independently on initial a(i).
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FORMULA
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a(n>2)=-1/a(n-1)+1/a(n-2), a(1)=1, a(2)=2, a(n)->-(-1)^n sqrt(2).
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EXAMPLE
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a(3)=-1/a(2)+1/a(1)=-1/2+1=1/2, therefore in the sequence, 3rd term is 2.
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CROSSREFS
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Cf. A076655.
Sequence in context: A084745 A036503 A109590 this_sequence A078239 A083113 A027498
Adjacent sequences: A074932 A074933 A074934 this_sequence A074936 A074937 A074938
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KEYWORD
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nonn,frac
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AUTHOR
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Zak Seidov (zakseidov(AT)yahoo.com), Oct 24 2002
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