A271835 Somos's sequence {a(5,n)} defined in comment in A018896: a(0)=a(1)= ... = a(11) = 1; for n>=12, a(n) = (a(n-1)*a(n-11) + a(n-6)^2)/a(n-12).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 11, 20, 36, 61, 97, 243, 425, 700, 1199, 2183, 4115, 14902, 43515, 102827, 214168, 418685, 1223440, 3053628, 9484929, 31351174, 95335734, 260010845, 1305343146, 4437434637, 12553187856, 35704506092

Offset: 0

Author

Vladimir Shevelev and Peter J. C. Moses, Apr 15 2016

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..368
• Eric Weisstein's World of Mathematics, Somos Sequence

Crossrefs

Cf. A018896, A006125, A006720, A102276, A271341, A271831, A271837, A271838, A271839.

Programs

Magma

[n le 12 select 1 else (Self(n-1)*Self(n-11) + Self(n-6)^2 )/Self(n-12): n in [1..50]]; // G. C. Greubel, Feb 21 2018

Mathematica

a[k_,n_]:=a[k,n]= If[n>2k+1,(a[k,(n-1)]*a[k,(n-2k-1)]+(a[k,(n-k-1)])^2 )/a[k,(n-2k-2)],1]; Map[a[5,#]&,Range[0,43]] (* Peter J. C. Moses, Apr 15 2016 *)
RecurrenceTable[{Table[a[i]==1,{i,0,11}],a[n]==(a[n-1]a[n-11]+a[n-6]^2)/ a[n-12]},a,{n,50}](* Harvey P. Dale, Sep 24 2021 *)

PARI

{a(n) = if(n< 12, 1, (a(n-1)*a(n-11) + a(n-6)^2)/a(n-12))};
for(n=0,50, print1(a(n), ", ")) \\ G. C. Greubel, Feb 21 2018

Extensions

More terms from Alois P. Heinz, Apr 15 2016