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

2, 2, 2, 7, 27, 377, 71252, 725274107, 19482315963330427, 1006792136061113006060577048627

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..14 (shortened by N. J. A. Sloane, Jan 13 2019)

Formula

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

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 *)

Prog

(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
(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

Crossrefs

Cf. A007660, A055937.

Sequence in context: A138757 A158927 A367857 * A087421 A309574 A132697

Adjacent sequences: A121255 A121256 A121257 * A121259 A121260 A121261

Keyword

nonn,easy

Author

Jonathan Vos Post, Aug 22 2006

Extensions

Data corrected by Vincenzo Librandi, Nov 14 2011

Status

approved