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A339233
Number of inequivalent colorings of oriented series-parallel networks with n colored elements.
1
1, 4, 21, 165, 1609, 19236, 266251, 4175367, 72705802, 1387084926, 28689560868, 638068960017, 15158039092293, 382527449091778, 10207466648995608, 286876818184163613, 8462814670769394769, 261266723355912507073, 8419093340955799898258, 282519424041100564770142
OFFSET
1,2
COMMENTS
Equivalence is up to permutation of the colors. Any number of colors may be used. See A339228 for additional details.
EXAMPLE
In the following examples elements in series are juxtaposed and elements in parallel are separated by '|'.
a(1) = 1: (1).
a(2) = 4: (11), (12), (1|1), (1|2).
a(3) = 21: (111), (112), (121), (122), (123), (1(1|1)), (1(1|2)), (1(2|2)), (1(2|3)), ((1|1)1), ((1|1)2), ((1|2)1), ((1|2)3), (1|1|1), (1|1|2), (1|2|3), (1|11), (1|12), (1|21), (1|22), (1|23).
PROG
(PARI) \\ See links in A339645 for combinatorial species functions.
cycleIndexSeries(n)={my(Z=x*sv(1), p=Z+O(x^2)); for(n=2, n, p=sEulerT(p^2/(1+p) + Z)-1); p}
InequivalentColoringsSeq(cycleIndexSeries(15))
CROSSREFS
Cf. A003430 (uncolored), A339226, A339228, A339229, A339287 (unoriented), A339645.
Sequence in context: A144010 A366184 A179496 * A107872 A008858 A217484
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Dec 22 2020
STATUS
approved