

guesscontinue[data_] :=
   Module[ {rec, r},
     rec = GuessMinRE[data, f[n]];
     If[ Head[rec] === Hold, Return[$Failed] ];
     r = Max[Cases[rec, f[n+i_] -> i, {0, Infinity}]];
     rec = rec /. n -> n - r;
     rhs = f[n] /. First[Solve[rec==0, f[n]]];
     rhs /. n -> Length[data] /. f[u_] :> data[[u + 1]]
   ];