A133400 a(0)=a(1)=a(2) = 1, thereafter a(n) = a(n-1)*a(n-2)*a(n-3) + 1.

1, 1, 1, 2, 3, 7, 43, 904, 272105, 10577265561, 2601826668310218121, 7488387181338771882437732599874506, 206081999881071045385328009597554265108557649484947339933019787

Offset: 0

Author

Jonathan Vos Post, Nov 24 2007, Nov 26 2007

Keywords

• easy
• nonn

Comments

A tribonacci analog of A001056.

a(13) has 115 digits. - R. J. Mathar, Dec 10 2007

Examples

			a(8) = a(7)*a(6)*a(5) + 1 = 904 * 43 * 7 + 1 = 272105.
a(9) ~ 2.60182667 * 10^18.
a(10) ~ 7.48838719 * 10^33.
a(11) ~ 2.06082 * 10^62.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..16

Crossrefs

Cf. A001056, A007660, A058265.

Programs

GAP

a:=[1,1,1];; for n in [4..15] do a[n]:=a[n-1]*a[n-2]*a[n-3]+1; od; a; # G. C. Greubel, Sep 20 2019

Magma

I:=[1,1,1]; [n le 3 select I[n] else Self(n-1)*Self(n-2)* Self(n-3) + 1: n in [1..15]]; // G. C. Greubel, Sep 20 2019

Maple

A133400 := proc(n) local i ; if n <= 2 then 1; else 1+mul( A133400(i),i=n-3..n-1) ; fi ; end: seq(A133400(n),n=0..15) ; # R. J. Mathar, Dec 10 2007

Mathematica

RecurrenceTable[{a[0]==1,a[1]==1,a[2]==1, a[n] == a[n-1]*a[n-2]*a[n-3] + 1},a,{n,0,15}] (* Vaclav Kotesovec, May 05 2015 *)
nxt[{a_,b_,c_}]:={b,c,a*b*c+1}; NestList[nxt,{1,1,1},15][[All,1]] (* Harvey P. Dale, Mar 05 2017 *)

PARI

m=15; v=concat([1,1,1], vector(m-3)); for(n=4, m, v[n]=v[n-1]*v[n-2] *v[n-3] +1 ); v \\ G. C. Greubel, Sep 20 2019

Sage

def a(n):
    if (n<3): return 1
    else: return a(n-1)*a(n-2)*a(n-3) + 1
[a(n) for n in (0..15)] # G. C. Greubel, Sep 20 2019

Formula

a(n) ~ c^(t^n), where c = 1.1004451797920944914628..., t = A058265 = 1.8392867552141611325518... . - Vaclav Kotesovec, May 05 2015

Extensions

More terms from R. J. Mathar, Dec 10 2007