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A340027 Number of inequivalent vertex colorings of connected graphs on n unlabeled vertices. 3
1, 1, 2, 7, 50, 520, 10665, 400220, 29204589, 4143245857, 1146827743079, 619412332805088, 653237982066620540, 1346571060160843394520, 5432476352054378478159877, 42947950068987980977264834190, 666212968663987333085874313873428, 20301440661023158546856805172595805762 (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
EXAMPLE
a(3) = 7 because there are 2 connected graphs on 3 vertices. The complete graph K_3 can be coloring in 3 ways (111, 112, 123) and the path graph P_3 can be colored in 4 ways (111, 112, 121, 123).
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(1+sLog(graphsSeries(15)))
CROSSREFS
Sequence in context: A139008 A058721 A363862 * A362340 A324513 A086902
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Jan 02 2021
STATUS
approved

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Last modified March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)