As part of the MRC summer school on cluster algebras in Snowbird (June 2014), there was a group of researchers interested in combinatorial and representation theoretic aspects of maximal green sequences. For their definition and main features on both of these perspectives, see this paper by Brüstle, Dupont and Pérotin.
This website provides a Dijkstra-like algorithm for computing maximal green sequences for skew-symmetrisable matrices. The code can be easily modified for using stopping levels within the search algorithm, please feel free to play around with it or drop me an email if you would like to know more details.
After loading these function, we can now compute all maximal green sequences for a given skew-symmetrisable matrix, assuming sign-coherence.
Use simple Sage commands to get a list of the length of these sequences. and a count for each length.
Get a count for each length in increasing order.
Note that all cells with an 'Evaluate'-button underneath can be altered - feel free to test the functions on (small enough) skew-symmetrisable matrices of your own choosing. Please feel free to contact me for comments and/or questions.