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A339287
Number of inequivalent colorings of unoriented series-parallel networks with n colored elements.
1
1, 4, 15, 105, 873, 9997, 134582, 2096206, 36391653, 693779666, 14346005530, 319042302578, 7579064231400, 191264021808301, 5103735168371201, 143438421861618397, 4231407420255210941, 130633362289335958866, 4209546674788934624394, 141259712052820378949746
OFFSET
1,2
COMMENTS
Equivalence is up to permutation of the colors and reversal of all parts combined in series. Any number of colors may be used. See A339282 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) = 15: (111), (112), (121), (123), (1(1|1)), (1(1|2)), (1(2|2)), (1(2|3)), (1|1|1), (1|1|2), (1|2|3), (1|11), (1|12), (1|22), (1|23).
PROG
(PARI) \\ See links in A339645 for combinatorial species functions.
B(n)={my(Z=x*sv(1), p=Z+O(x^2)); for(n=2, n, p=sEulerT(p^2/(1+p) + Z)-1); p}
cycleIndexSeries(n)={my(Z=x*sv(1), q=sRaise(B((n+1)\2), 2), s=x^2*sv(2)+q^2/(1+q), p=Z+O(x^2), t=p); for(n=1, n\2, t=Z + q*(1 + p); p=Z + sEulerT(t+(s-sRaise(t, 2))/2) - t - 1); (p+t-Z+B(n))/2}
InequivalentColoringsSeq(cycleIndexSeries(15))
CROSSREFS
Cf. A339225 (uncolored), A339233 (oriented), A339280, A339282, A339283, A339645.
Sequence in context: A356524 A289489 A221095 * A081548 A207163 A009315
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Dec 22 2020
STATUS
approved