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A340024 Number of inequivalent vertex colorings of graphs on n unlabeled vertices. 3
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)}

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

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Last modified May 24 00:13 EDT 2022. Contains 353993 sequences. (Running on oeis4.)