A271838 Somos's sequence {a(8,n)} defined in comment in A018896: a(0)=a(1)= ... = a(17) = 1; for n>=18, a(n) = (a(n-1)*a(n-17)+ a(n-9)^2)/a(n-18).

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, 14, 23, 39, 64, 100, 149, 213, 294, 688, 1130, 1683, 2484, 3800, 6100, 10143, 17082, 28584, 87352, 234714, 521145, 1013424, 1809100, 3067659, 5075784, 8375940, 22379904, 47848348

Offset

0,19

Links

Seiichi Manyama, Table of n, a(n) for n = 0..510

Eric Weisstein's World of Mathematics, Somos Sequence

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[8, #]&, Range[0, 50]] (* Peter J. C. Moses, Apr 15 2016 *)
RecurrenceTable[{a[0]==a[1]==a[2]==a[3]==a[4]==a[5]==a[6]==a[7]==a[8]==a[9]== a[10]==a[11]==a[12]==a[13]==a[14]==a[15]==a[16]==a[17]==1, a[n]==(a[n-1]a[n-17]+ a[n-9]^2)/a[n-18]}, a, {n, 60}] (* Harvey P. Dale, Jun 30 2023 *)

Prog

(PARI) {a(n) = if(n< 18, 1, (a(n-1)*a(n-17) + a(n-9)^2)/a(n-18))};
for(n=0, 40, print1(a(n), ", ")) \\ G. C. Greubel, Feb 21 2018
(Magma) [n le 18 select 1 else (Self(n-1)*Self(n-17) + Self(n-9)^2 )/Self(n-18): n in [1..40]]; // G. C. Greubel, Feb 21 2018

Crossrefs

Cf. A018896, A006125, A006720, A102276, A271341, A271835, A271831, A271837, A271839.

Sequence in context: A134933 A136040 A306014 * A194846 A194057 A372317

Adjacent sequences: A271835 A271836 A271837 * A271839 A271840 A271841

Keyword

nonn

Author

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

Status

approved