Somos Sequence

Author

Eric W. Weisstein
April 28, 2006

This notebook downloaded from http://mathworld.wolfram.com/notebooks/IntegerSequences/SomosSequence.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/SomosSequence.html.

©2006 Wolfram Research, Inc. except for portions noted otherwise

Code

Somos[k_Integer,n_Integer]:=1/;0≤n≤k-1
Somos[k_Integer,n_Integer]:=Somos[k,n]=Module[{j},
Sum[((Somos[k,n-j]Somos[k,n-(k-j)])/(Somos[k,n-k])),{j,Floor[k/2]}]
]

Enumeration

Table[Somos[k,n],{k,2,7},{n,0,15}]//TableForm

Fractions

Table[SomosFraction[i],{i,8,30}]

a=%;Table[a[[i+1]]-a[[i]],{i,1,Length[a]-1}]