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

0,13

Links

Seiichi Manyama, Table of n, a(n) for n = 0..368

Eric Weisstein's World of Mathematics, Somos Sequence

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 *)

Prog

(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
(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

Crossrefs

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

Sequence in context: A174821 A033086 A059768 * A118599 A178531 A358254

Adjacent sequences: A271832 A271833 A271834 * A271836 A271837 A271838

Keyword

nonn

Author

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

Extensions

More terms from Alois P. Heinz, Apr 15 2016

Status

approved