The Raptis algorithm works perfectly for me, for valid inputs, which the user has to take care of. So, great work, 5 stars for the algorithm.

Concerning the Opdyke paper, regards the algorithms, 5 stars here as well.

The formulas appear problematic, however. The presumably "novel" formulas concerning integer compositions are seemingly taken from

Heubach, Silvia, Mansour, Toufik, Compositions of n with parts in a set

Thereom 2.1, which is reference 6 or so in the paper. So, there has been no "open problem" that the paper has solved. But, as Jasper Baxxter points out, we're Matlab USERS, not rocket scientists. So, I don't care for the counting formulas as long as the algo is correct. Overall, 5 stars from me.