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

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

Offset: 0

Author

Vincenzo Librandi, Sep 30 2015

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..17

Crossrefs

Cf. A007660, A055937.

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