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Search: id:A007660
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| A007660 |
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a(n) = a(n-1)*a(n-2) + 1.
(Formerly M0853)
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+0
7
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| 0, 0, 1, 1, 2, 3, 7, 22, 155, 3411, 528706, 1803416167, 953476947989903, 1719515742866809222961802, 1639518622529236077952144318816050685207, 2819178082162327154499022366029959843954512194276761760087463015
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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If we omit the first three terms of the sequence, a(n)/a(n-1) can be expressed as the continued fraction [a(n-2); a(n-1)]. - Eric Angelini (eric.angelini(AT)kntv.be), Feb 10 2005
This may be regarded as a multiplicative dual of the Fibonacci sequence A000045. Write Fibonacci's formula as F(0)=0, F(1)=1; F(n)=[F(n-1)+F(n-2)]*1 with n>1. Swap '+' and '*' and we have the present sequence! - B. Joshipura (bhushit(AT)yahoo.com), Aug 29 2007
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fib. Quart., 11 (1973), 429-437.
B. Joshipura, My non-mathematician's posting
S. Kak, The Golden Mean and the Physics of Aesthetics
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FORMULA
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a(n) is asymptotic to c^(phi^n) where phi=(1+sqrt(5))/2 and c=1.1130579759029319... - Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 26 2003
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MATHEMATICA
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a[0] = a[1] = 0; a[n_] := a[n - 1]*a[n - 2] + 1; Table[ a[n], {n, 0, 15} ]
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CROSSREFS
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Sequence in context: A077210 A151908 A072214 this_sequence A158055 A156615 A158054
Adjacent sequences: A007657 A007658 A007659 this_sequence A007661 A007662 A007663
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com)
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