A271839 Somos's sequence {a(9,n)} defined in comment in A018896: a(0)= a(1) = ... = a(19) = 1; for n >= 20, a(n) = (a(n-1)*a(n-19) + a(n-10)^2)/a(n-20).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 15, 24, 40, 65, 101, 150, 214, 295, 395, 911, 1479, 2164, 3105, 4571, 7033, 11252, 18383, 30095, 48707, 141866, 372815, 816479, 1567804, 2757573, 4585139, 7385515

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..555
• Eric Weisstein's World of Mathematics, Somos Sequence

Crossrefs

Cf. A018896, A006125, A006720, A102276, A271341, A271835, A271831, A271837, A271838.

Programs

Magma

[n le 20 select 1 else (Self(n-1)*Self(n-19) + Self(n-10)^2 )/Self(n-20): 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[9,#]&,Range[0,70]] (* Peter J. C. Moses, Apr 15 2016 *)

PARI

{a(n) = if(n< 20, 1, (a(n-1)*a(n-19) + a(n-10)^2)/a(n-20))};
for(n=0,50, print1(a(n), ", ")) \\ G. C. Greubel, Feb 21 2018