cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A121258 a(n) = a(n-1)*a(n-2)*a(n-3) - 1 with a(0)=a(1)=a(2)=2.

Original entry on oeis.org

2, 2, 2, 7, 27, 377, 71252, 725274107, 19482315963330427, 1006792136061113006060577048627
Offset: 0

Views

Author

Jonathan Vos Post, Aug 22 2006

Keywords

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?

Crossrefs

Programs

  • Magma
    I:=[2,2,2]; [n le 3 select I[n] else Self(n-1)*Self(n-2)* Self(n-3)-1: n in [1..12]]; // Vincenzo Librandi, Nov 14 2011
    
  • Mathematica
    RecurrenceTable[{a[0]==a[1]==a[2]==2, a[n] == a[n-1]*a[n-2]*a[n-3] - 1}, a, {n, 0, 15}] (* G. C. Greubel, Jun 07 2019 *)
    nxt[{a_,b_,c_}]:={b,c,a*b*c-1}; NestList[nxt,{2,2,2},10][[All,1]] (* Harvey P. Dale, Jun 25 2020 *)
  • PARI
    a(n) = if(n<3, 2, a(n-1)*a(n-2)*a(n-3) - 1);
    vector(12, 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-2)*a(n-3) - 1
    [a(n) for n in (0..12)] # G. C. Greubel, Jun 07 2019

Formula

a(n) ~ c^(A058265^n), where c = 1.3319334322065642848267... - Vaclav Kotesovec, Jun 15 2019

Extensions

Data corrected by Vincenzo Librandi, Nov 14 2011

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

Original entry on oeis.org

2, 2, 2, 3, 5, 9, 26, 129, 1160, 30159, 3890510, 4512991599, 136107313634240, 529526864767147062399, 2389750292138943783804215786000, 325262492519671886357848434144628838112639999
Offset: 0

Views

Author

Jonathan Vos Post, Aug 22 2006

Keywords

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 ?

Crossrefs

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

A262714 a(n) = a(n-1)*a(n-2) + 1, with a(0) = a(1) = 2.

Original entry on oeis.org

2, 2, 5, 11, 56, 617, 34553, 21319202, 736642386707, 15704627843968647815, 11568694537326272321321120595206, 181682042349262169758803442669575561298555791374891, 2101824050856189730969091901210449068013789839106586804501928241686514359003372547
Offset: 0

Views

Author

Vincenzo Librandi, Sep 30 2015

Keywords

Crossrefs

Programs

  • Magma
    [n le 2 select 2 else Self(n-1)*Self(n-2)+1: n in [1..20]];
    
  • Mathematica
    RecurrenceTable[{a[0]==a[1]==2, a[n]==a[n-1]*a[n-2] +1}, a, {n, 0, 20}]
  • PARI
    a(n) = if(n<2, 2, 1 + a(n-1)*a(n-2))
    vector(20, n, a(n-1)) \\ Altug Alkan, Sep 30 2015
    
  • PARI
    {a(n) = if( n<2, 2 * (n>=0), self()(n-1) * self()(n-2) + 1)}; /* Michael Somos, Oct 02 2015 */
    
  • Sage
    def a(n):
        if (n==0 or n==1): return 2
        else: return a(n-1)*a(n-2) +1
    [a(n) for n in (0..20)] # G. C. Greubel, Jun 07 2019
Showing 1-3 of 3 results.