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

Author

Andrew Howroyd, Dec 22 2020

Keywords

• nonn

Comments

Equivalence is up to permutation of the colors. Any number of colors may be used. See A339228 for additional details.

Examples

			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).
		

Crossrefs

Cf. A003430 (uncolored), A339226, A339228, A339229, A339287 (unoriented), A339645.

Programs

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))