Why sequences of marginal interest are bad

[Ralf Stephan]

You wrote 
> As, for instance, Fibonacci numbers as sums of natural numbers, triangular
> numbers, tetrahedral numbers, ...?  Or A048888 as the sum of Fibonacci,
> tribonacci, tetranacci, ...?

Even simpler, like n^2 + 1 the sum of the squares and the "all one"
sequence. At least, as long one uses simple pattern matching for
the search which is the fastest. On the other end of searching
algorithms, one *could use the LLL to find for any sum of sequences
but, even if it's a fast algorithm, it's not fast enough to handle
tens of thousands of sequences.

> Is there a "spectrum" of the OEIS as to the distribution of number of seqs
> related by some standard set oif transformations to other sequences? You are
> saying that there is a peak in the eigenspectrum at 2, and more beyond that.
> Assuming that her spectrum is known from your amazing work so fare, does
> that quantify the time-complexity of continuing the great work as a function
> of number of seqs?

I have no numbers, this is all from just working with the OEIS. I don't
think there is a peak at 2.

You know you can cluster sequences into those with polynomial formula, 
those with rational g.f., D-finite, prime related, divide-and-conquer
recurrent (I call them "bifurcative"), theta functions plus modular
forms and many other smaller groups. From experience, there is not much
overlap between the groups. You can find in-group combinations and
between-group combinations so there is no recipe.

And then, there are those without any simple relation. 

And then, there are those without any relation. Most fun!


ralf