A340024 - OEIS

A340024

Number of inequivalent vertex colorings of graphs on n unlabeled vertices.

1, 1, 4, 14, 89, 788, 13712, 459380, 31395800, 4304547500, 1170501781632, 626269787446920, 657129205489027200, 1350883625562244545584, 5441806297331472273603040, 42987375826579901036722653600, 666538741644051928632441002162384, 20306710978262167791045247702178986496

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

COMMENTS

Equivalence is up to permutation of the colors. Adjacent vertices may have the same color.

LINKS

Table of n, a(n) for n=0..17.

PROG

(PARI) \\ See links in A339645 for combinatorial species functions.

edges(v) = {sum(i=2, #v, sum(j=1, i-1, gcd(v[i], v[j]))) + sum(i=1, #v, v[i]\2)}

graphsCycleIndex(n)={my(s=0); forpart(p=n, s+=permcount(p) * 2^edges(p) * sMonomial(p)); s/n!}

graphsSeries(n)={sum(k=0, n, graphsCycleIndex(k)*x^k) + O(x*x^n)}