A121256 a(n) = a(n-1)*a(n-3) - 1, starting with a(0)=a(1)=a(2)=2.

2, 2, 2, 3, 5, 9, 26, 129, 1160, 30159, 3890510, 4512991599, 136107313634240, 529526864767147062399, 2389750292138943783804215786000, 325262492519671886357848434144628838112639999

Offset

0,1

Comments

Analog of A055937 a(n) = a(n-1)*a(n-2) - 1. What is the equivalent continued fraction and asymptotic representation, by analogy to A007660 a(n) = a(n-1)*a(n-2) + 1 ?

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..22 (shortened by N. J. A. Sloane, Jan 13 2019)

Mathematica

RecurrenceTable[{a[0]==a[1]==a[2]==2, a[n]==a[n-1]a[n-3]-1}, a, {n, 20}] (* Harvey P. Dale, Sep 02 2016 *)

Prog

(Magma) I:=[2, 2, 2]; [n le 3 select I[n] else Self(n-1)*Self(n-3)-1: n in [1..20]]; // Vincenzo Librandi, Nov 14 2011
(PARI) a(n) = if(n<3, 2, a(n-1)*a(n-3) - 1);
vector(20, n, n--; a(n)) \\ G. C. Greubel, Jun 07 2019
(Sage)
def a(n):
    if (n==0 or n==1 or n==2): return 2
    else: return a(n-1)*a(n-3) -1
[a(n) for n in (0..20)] # G. C. Greubel, Jun 07 2019

Crossrefs

Cf. A007660, A055937.

Sequence in context: A243358 A059690 A330310 * A022867 A268595 A299019

Adjacent sequences: A121253 A121254 A121255 * A121257 A121258 A121259

Keyword

easy,nonn

Author

Jonathan Vos Post, Aug 22 2006

Extensions

Corrected and extended by Vincenzo Librandi, Nov 14 2011

Status

approved