A122055 A Somos 9-type recurrence: a(n) = (3*a(n-1)*a(n-8) - a(n-4)*a(n-5))/a(n-9), with a(0)=...=a(8)=1.

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 5, 14, 41, 121, 353, 989, 2393, 9397, 49121, 342793, 2842633, 24619238, 211654405, 1731275594, 11581792513, 107195509553, 1126517154817, 16124559341513, 342648008481505, 8465982933121657, 213444061953471233

Offset: 0

Author

Roger L. Bagula, Sep 13 2006

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A122025.

Programs

GAP

a:= function(n)
    if n<10 then return 1;
    else return (3*a(n-1)*a(n-8) - a(n-4)*a(n-5))/a(n-9);
    fi;
  end;
List([0..35], n-> a(n) ); # G. C. Greubel, Oct 03 2019

Magma

[n le 10 select 1 else (3*Self(n-1)*Self(n-8) - Self(n-4)*Self(n-5))/Self(n-9): n in [1..35]]; // G. C. Greubel, Oct 03 2019

Maple

a:= proc (n) option remember;
   if n < 9 then 1
   else (3*a(n-1)*a(n-8) - a(n-4)*a(n-5))/a(n-9)
   fi;
end proc;
seq(a(n), n=0..35); # G. C. Greubel, Oct 03 2019

Mathematica

a[n_]:= a[n]= If[n<9, 1, (3*a[n-1]*a[n-8] -a[n-4]*a[n-5])/a[n-9]];
Table[a[n], {n, 0, 30}] (* modified by G. C. Greubel, Oct 03 2019 *)
nxt[{a_,b_,c_,d_,e_,f_,g_,h_,i_}]:={b,c,d,e,f,g,h,i,(3i*b-f*e)/a}; NestList[nxt,PadRight[{},9,1],30][[;;,1]] (* Harvey P. Dale, Jun 05 2024 *)

PARI

m=35; v=concat([1,1,1,1,1,1,1,1,1], vector(m-9)); for(n=10, m, v[n] = (3*v[n-1]*v[n-8] - v[n-4]*v[n-5])/v[n-9] ); v \\ G. C. Greubel, Oct 03 2019

Sage

def a(n):
    if n<10: return 1
    else: return (3*a(n-1)*a(n-8) - a(n-4)*a(n-5))/a(n-9)
[a(n) for n in (0..35)] # G. C. Greubel, Oct 03 2019

Formula

a(n) = (3*a(n-1)*a(n-8) - a(n-4)*a(n-5))/a(n-9).

Extensions

Name edited and offset changed by G. C. Greubel, Oct 03 2019