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

0,21

Links

Seiichi Manyama, Table of n, a(n) for n = 0..555

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[9, #]&, Range[0, 70]] (* Peter J. C. Moses, Apr 15 2016 *)

Prog

(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
(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

Crossrefs

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

Sequence in context: A254649 A261293 A177872 * A290144 A115060 A378647

Adjacent sequences: A271836 A271837 A271838 * A271840 A271841 A271842

Keyword

nonn

Author

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

Status

approved