Counting n-gons

[T. D. Noe]

>I agree; the order of the sides should really be significant, up to
>rotation and reflection.
>
>The sequence with this definition for quadrilaterals is A05788.
>Sequences for polygons with more sides do not seem to be in the OEIS.

I think A05788 must be an error.  Not enough digits.

I agree that the order is important.  The sequences A062890, A069906,
A069907, and my new A124278 assume the order of the edge lengths is
increasing.  This is assumed by the Andrews et al paper also.  For the
general case, you windup counting necklaces.  From Mathematica,

ListNecklaces[4, {3,2,1,1}, Dihedral]

results in {{3,2,1,1}, {1,2,1,3}}.  This means, counting {2,2,2,1}, that
there are 3 quadrilaterals of perimeter 7.

Tony