A271837 Somos's sequence {a(7,n)} defined in comment in A018896: a(0)=a(1)= ... = a(15) = 1; for n>=16, a(n) = (a(n-1)*a(n-15)+ a(n-8)^2)/a(n-16).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 13, 22, 38, 63, 99, 148, 212, 505, 842, 1284, 1966, 3153, 5312, 9200, 15968, 51401, 141522, 319386, 631223, 1149722, 2003800, 3442200, 9402302, 20908517, 55671036, 164685883, 466783858

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..463
• Eric Weisstein's World of Mathematics, Somos Sequence

Crossrefs

Cf. A018896, A006125, A006720, A102276, A271341, A271831, A271835, A271838, A271839.

Programs

Magma

[n le 16 select 1 else (Self(n-1)*Self(n-15) + Self(n-8)^2 )/Self(n-16): n in [1..50]]; // G. C. Greubel, Feb 21 2018

Mathematica

a[k_,n_]:=a[k,n] = If[n>2*k+1,(a[k,(n-1)]*a[k,(n-2*k-1)]+(a[k,(n-k-1)])^2 )/a[k,(n-2*k-2)],1]; Map[a[7,#]&,Range[0,50]] (* Peter J. C. Moses, Apr 15 2016 *)

PARI

{a(n) = if(n< 16, 1, (a(n-1)*a(n-15) + a(n-8)^2)/a(n-16))};
for(n=0,50, print1(a(n), ", ")) \\ G. C. Greubel, Feb 21 2018