  The On-Line Encyclopedia Of Integer Sequences , that wonderful resource that
most combinatorialists, and many other mathematicians and scientists, use at
least once a day, is a treasure trove of mathematical information, and, one of
its charms is that it contains many intriguing conjectures. But one should be
on one's guard, because some of the conjectures are either already theorems, or
can be routinely proved. In this case study we demonstrate, and actually fully
implement (in an accompanying Maple package), how to turn many conjectures made
in the OEIS by R.J. Mathar, regarding linear recurrences satisfies by a certain
class of sequences, into fully rigorously-proved theorems, but we argue, that
one should not emulate us, and while it is nice to have one example, of an
algorithm to actually construct proofs (that are known to exist by a priori
theoretical reasons), life is too short to do it in all cases, and hence we
propose a new category for the OEIS, that of "provable conjecture", as opposed
to "proved conjecture" (alias theorem).
