A268199 Somos's sequence {b(3,n)} defined in comment in A078495: a(0)=a(1)=...=a(8)=1; for n>=9, a(n)=(a(n-1)*a(n-8)+a(n-4)*a(n-5))/a(n-9).

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 7, 13, 25, 45, 125, 233, 419, 805, 2252, 8343, 23554, 55889, 195533, 514781, 1769117, 6540689, 31873013, 162776741, 568710437, 1840702289, 10169970946, 53308101423, 363030298268, 1933899726085, 12286029791291

Offset: 0

Author

Vladimir Shevelev and Peter J. C. Moses, Apr 16 2016

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..292

Crossrefs

Cf. A006721, A078495, A271948.

Programs

Magma

[n le 9 select 1 else (Self(n-1)*Self(n-8) + Self(n-4)*Self(n-5)) /Self(n-9): n in [1..40]]; // G. C. Greubel, Feb 21 2018

Mathematica

a[k_,n_]:=a[k,n]=If[n>2k+2,(a[k,(n-1)]*a[k,(n-2k-2)]+a[k,(n-k-1)]*a[k,(n-k-2)])/a[k,(n-2k-3)],1];
Map[a[3,#]&,Range[0,50]] (* Peter J. C. Moses, Apr 16 2016 *)
a[ n_] := a[n] = Which[ n<0, a[8-n], n<9, 1, True, (a[n - 1] a[n - 8] + a[n - 4] a[n - 5]) / a[n - 9]]; (* Michael Somos, Nov 16 2016 *)

PARI

{a(n) = if(n<= 8, 1, (a(n-1)*a(n-8)+a(n-4)*a(n-5))/a(n-9))};
for(n=1,40, print1(a(n), ", ")) \\ G. C. Greubel, Feb 21 2018

Formula

a(n) = a(8-n) for all n in Z. - Michael Somos, Nov 16 2016