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

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)}
InequivalentColoringsSeq(graphsSeries(15))

Crossrefs

Cf. A000088, A340022, A340023, A340027.

Sequence in context: A330465 A202139 A331637 * A190481 A316414 A268689

Adjacent sequences: A340021 A340022 A340023 * A340025 A340026 A340027

Keyword

nonn

Author

Andrew Howroyd, Jan 01 2021

Status

approved