A339287 Number of inequivalent colorings of unoriented series-parallel networks with n colored elements.

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.

Links

Table of n, a(n) for n=1..20.

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

Adjacent sequences: A339284 A339285 A339286 * A339288 A339289 A339290

Keyword

nonn

Author

Andrew Howroyd, Dec 22 2020

Status

approved