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

Author

Jonathan Vos Post, Aug 22 2006

Keywords

• easy
• nonn

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)

Crossrefs

Cf. A007660, A055937.

Programs

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

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 *)

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

Extensions

Corrected and extended by Vincenzo Librandi, Nov 14 2011