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 A007660 a(n) = a(n-1)*a(n-2) + 1 with a(0) = a(1) = 0. (Formerly M0853) 13
 0, 0, 1, 1, 2, 3, 7, 22, 155, 3411, 528706, 1803416167, 953476947989903, 1719515742866809222961802, 1639518622529236077952144318816050685207, 2819178082162327154499022366029959843954512194276761760087463015 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 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, 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 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..19 (shortened by N. J. A. Sloane, Jan 13 2019) 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, arXiv:physics/0411195 [physics.hist-ph], 2004. FORMULA a(n) is asymptotic to c^(phi^n) where phi = (1 + sqrt(5))/2 and c = A258113 = 1.1130579759029319... - Benoit Cloitre, Sep 26 2003 b(n) = a(n+1) is a divisibility sequence. - Michael Somos, Dec 29 2012 EXAMPLE b(10) / b(5) = 1803416167 / 7 = 257630881. - Michael Somos, Dec 29 2012 MATHEMATICA a = a = 0; a[n_] := a[n - 1]*a[n - 2] + 1; Table[ a[n], {n, 0, 15} ] RecurrenceTable[{a==a==0, a[n]==a[n-1]a[n-2]+1}, a, {n, 20}] (* Harvey P. Dale, Nov 12 2011 *) 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 (Haskell) a007660 n = a007660_list !! n a007660_list = 0 : 0 : map (+ 1)                        (zipWith (*) a007660_list \$ tail a007660_list) -- Reinhard Zumkeller, Jan 17 2015 (Maxima) a(n) := if (n=0 or n=1) then 0 else a(n-1)*a(n-2)+1 \$ makelist(a(n), n, 0, 18); /* Emanuele Munarini, Mar 24 2017 */ CROSSREFS Cf. A250309, A253853, A258113. Sequence in context: A151908 A072214 A233535 * A158055 A156615 A158054 Adjacent sequences:  A007657 A007658 A007659 * A007661 A007662 A007663 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified July 20 11:28 EDT 2019. Contains 325180 sequences. (Running on oeis4.)