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A022405 a(n) = a(n-1)*a(n-2) - a(n-3), with a(1) = 0, a(2) = 1, a(3) = 2. 8
0, 1, 2, 2, 3, 4, 10, 37, 366, 13532, 4952675, 67019597734, 331926286207224918, 22245566178948766568816183137, 7383888166355511098764350563784314022618210032 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Theorem 1.1 of Hare et al. (2010, 2011) involves a shifted version of this sequence and the Fibonacci sequence A000045. (The program by Alonso del Arte below does involve a shifted version of this sequence.) - Petros Hadjicostas, May 11 2019

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..21

Kevin G. Hare, Ian D. Morris, Nikita Sidorov, and Jacques Theys, An explicit counterexample to the Lagarias-Wang finiteness conjecture, arXiv:1006.2117 [math.OC], 2010-2011.

Kevin G. Hare, Ian D. Morris, Nikita Sidorov, and Jacques Theys, An explicit counterexample to the Lagarias-Wang finiteness conjecture, Advances in Mathematics 226 (2011), 4667-4701.

FORMULA

It appears that lim_{n->infinity} log(a(n))/phi^n = 0.07743008049000107520747623421744398272089261907514..., where phi = (1 + sqrt(5))/2 is the golden ratio A001622. - Petros Hadjicostas and Jon E. Schoenfield, May 11 2019

MATHEMATICA

a[1] = 0; a[2] = 1; a[3] = 2; a[n_] := a[n] = a[n - 1] a[n - 2] - a[n - 3]; Table[a[n], {n, 1, 15}] (* Alonso del Arte, Jan 31 2011 *)

PROG

(MAGMA) I:=[0, 1, 2]; [n le 3 select I[n] else Self(n-1)*Self(n-2) - Self(n-3): n in [1..15]];  // G. C. Greubel, Mar 01 2018

CROSSREFS

Cf. A001622, A061021, A061292, A072878, A072879, A072880, A178768.

Sequence in context: A239967 A307891 A205118 * A309895 A270744 A093927

Adjacent sequences:  A022402 A022403 A022404 * A022406 A022407 A022408

KEYWORD

easy,nonn

AUTHOR

Robert G. Wilson v, Jul 05 2000

EXTENSIONS

Name clarified by Michel Marcus, May 10 2019

STATUS

approved

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Last modified January 27 04:57 EST 2020. Contains 331291 sequences. (Running on oeis4.)