(nauty) geng -c -D4 ${n} $[${n}-1]:$[${n}-1] -q | multig -m3 -D4 -u
(PARI) \\ here S is MSET_k comb class of g
S(g, n, k)={polcoeff(exp( sum(i=1, k, (y^i + O(y*y^k))*subst(g + O(x*x^(n\i)), x, x^i)/i )), k, y) + O(x*x^n)}
R(n)={my(f, g, h); f=g=h=O(x); for(n=1, n, h = x*(1+f); g = h + x*(S(f, n, 2) + g); f = g + x*(S(f, n, 3) + f*g + h)); [f, g, h]}
seq(n)={my(t=R(n), f=t[1], g=t[2], h=t[3]); Vec(f + x*(S(f, n, 4) + g*S(f, n, 2) + S(g, n, 2) + f*h) + (subst(f+g+h+O(x*x^(n\2)), x, x^2) - f^2 - g^2 - h^2)/2)} \\
Andrew Howroyd, May 26 2018
