0,4

A discrete analogue of the derivative of t(x) = tetration base e, since t'(x) = t(x) * t(x-1) * t(x-2) * ... y = y * exp(y) * exp(exp(y)) * ... * t(x) This sequence satisfies almost the same equation but the derivative is replaced by a difference, comparable to the relations between differential equations and their associated difference equations. - Raes Tom (tommy1729(AT)hotmail.com), Aug 06 2008

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

M. E. Mays, Iterating the division algorithm, Fib. Quart., 25 (1987), 204-213.

a(0) = a(1) = 1, a(2) = 2; a(n) = a(n-1)*a(n-2)*a(n-3)*... + a(n-1). - Raes Tom (tommy1729(AT)hotmail.com), Aug 06 2008

The sequence grows like a doubly exponential function, similar to Sylvester's sequence. In fact we have the asymptotic form : a(n) ~ e ^ (Phi ^ n) where e and Phi are the best possible constants. - Raes Tom (tommy1729(AT)hotmail.com), Aug 06 2008

a(5) = 12 since 12 = 1*2*4 + 4

a=0; b=1; lst={a, b}; Do[c=a*b+b; AppendTo[lst, c]; a=b; b=c, {n, 3*3!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 13 2009]

Cf. A007807.

Cf. A000058, A001622, A001113, A102575, A096436, A111129.

Sequence in context: A118456 A013202 A004400 this_sequence A136512 A137160 A013207

Adjacent sequences: A005828 A005829 A005830 this_sequence A005832 A005833 A005834

nonn,easy,nice

N. J. A. Sloane (njas(AT)research.att.com), Jeffrey Shallit

Edited by N. J. A. Sloane (njas(AT)research.att.com), Aug 29 2008 at the suggestion of R. J. Mathar