A numerical study of L-convex polyominoes and 201-avoiding ascent sequences

For L-convex polyominoes we give the asymptotics of the generating function coefficients, obtained by analysis of the coefficients derived from the functional equation given by Castiglione et al. \cite{CFMRR7}. For 201-avoiding ascent sequences, we conjecture the solution, obtained from the first 23 coefficients of the generating function. The solution is D-finite, indeed algebraic. The conjectured solution then correctly generates all subsequent coefficients. We also obtain the asymptotics, both from direct analysis of the coefficients, and from the conjectured solution. As well as presenting these new results, our purpose is to illustrate the methods used, so that they may be more widely applied.
Comment: 11 pages, 12 figures, accepted in S\'eminaire Lotharingien de Combinatoire, vol. 87B, 2023