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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
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
Sequence in context: A330465 A202139 A331637 * A190481 A316414 A268689
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Jan 01 2021
STATUS
approved

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Last modified March 19 04:26 EDT 2024. Contains 370952 sequences. (Running on oeis4.)