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A339287
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Number of inequivalent colorings of unoriented series-parallel networks with n colored elements.
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1
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1, 4, 15, 105, 873, 9997, 134582, 2096206, 36391653, 693779666, 14346005530, 319042302578, 7579064231400, 191264021808301, 5103735168371201, 143438421861618397, 4231407420255210941, 130633362289335958866, 4209546674788934624394, 141259712052820378949746
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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).
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PROG
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(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))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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