the sequence A006743

[Max]

Alec Mihailovs wrote:
>> I'm not familiar with gfun so I wonder
>> if the recurrences found by gfun or by your program have a 
>> (computer-based) proof or they are purely empirical?
> 
> The list of numbers entered in gfun[listtorec] satisfies the recurrence. 
> There can't be any proof for the extension of the recurrences on other 
> values (not entered in Maple).

It is possible to find recurrences based on a given generating function rather than elements of a sequence.
Since g.f. completely defines the sequence, it would be possible to produce a proof for the recurrences.
Is there any package for such computations?

As of gfun, if it uses only a limited amount of sequence's elements (as you said), it cannot give us any proof.

Max