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A007660
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a(n) = a(n-1)*a(n-2)+1 with a(0)=a(1)=0 .
(Formerly M0853)
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7
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0, 0, 1, 1, 2, 3, 7, 22, 155, 3411, 528706, 1803416167, 953476947989903, 1719515742866809222961802, 1639518622529236077952144318816050685207, 2819178082162327154499022366029959843954512194276761760087463015
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| 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
| N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..25
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
| 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
| a[0] = a[1] = 0; a[n_] := a[n - 1]*a[n - 2] + 1; Table[ a[n], {n, 0, 15} ]
RecurrenceTable[{a[0]==a[1]==0, a[n]==a[n-1]a[n-2]+1}, a, {n, 20}] (* From Harvey P. Dale, Nov 12 2011 *)
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PROG
| (MAGMA) I:=[0, 0]; [n le 2 select I[n] else Self(n-1)*Self(n-2)+1: n in [1..20]]; // Vincenzo Librandi, Nov 14 2011
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CROSSREFS
| Sequence in context: A077210 A151908 A072214 * A158055 A156615 A158054
Adjacent sequences: A007657 A007658 A007659 * A007661 A007662 A007663
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com)
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