A339233 Number of inequivalent colorings of oriented series-parallel networks with n colored elements.

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.

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) = 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

Adjacent sequences: A339230 A339231 A339232 * A339234 A339235 A339236

Keyword

nonn

Author

Andrew Howroyd, Dec 22 2020

Status

approved