login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 19 22:34 EDT 2024. Contains 374441 sequences. (Running on oeis4.)