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Abstract for Tiffany M. Barnes and Carla D. Savage, A Recurrence for Counting Graphical Partitions
 
In this paper, we give a recurrence to enumerate the set $G(n)$
of partitions of a positive even integer $n$ which are
the degree sequences of simple graphs.  The recurrence gives
rise to an algorithm to compute the number of elements of $G(n)$ in time $O(n^4)$ using space $O(n^3)$.
This appears to be the first  method for computing $|G(n)|$ in time bounded
by a polynomial in $n$, and it has enabled us to tabulate $|G(n)|$ for even
$n \leq 220$.
 
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