is sporadically impressive: In[127]:= FindSequenceFunction[Table[2^n - 1/n, {n, 11}], n] Out[127]= (-1 + 2^n n)/n In[133]:= FindSequenceFunction[Table[3^n/n - 2^n, {n, 11}], n] Out[133]= FindSequenceFunction[{1, 1/2, 1, 17/4, 83/5, 115/2, 1291/7, 4513/8, 1675, 48809/10, 154619/11}, n] In[130]:= FindSequenceFunction[{1, 2, 4, 8, 15}, n] Out[130]= 1/6 (8 n - 3 n^2 + n^3) In[131]:= Table[2^n/%, {n, 11}] Out[131]= {2, 2, 2, 2, 32/15, 32/13, 64/21, 4, 512/93, 512/65, 128/11} In[132]:= FindSequenceFunction[%, n] Out[132]= (3 2^(1 + n))/(n (8 - 3 n + n^2)) In[156]:= FindSequenceFunction[Table[1/(3^n - n), {n, 12}], n] Out[156]= FindSequenceFunction[{1/2, 1/7, 1/24, 1/77, 1/238, 1/723, 1/ 2180, 1/6553, 1/19674, 1/59039, 1/177136, 1/531429}, n] Is there known a generalization of reciprocal differences, say, that can detect rational_function(n,2^n,(-1)^n,Fib(n),...)? --rwg I have one that can detect Fibonacci[6*n]*Fibonacci[n]/Fibonacci[3*n]/Fibonacci[2*n] - Fibonacci[3*n]/Fibonacci[n] ;-)