  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.
