A339646 Number of inequivalent leaf colorings of series-reduced planted trees with n leaves using at most 2 colors.

1, 2, 5, 22, 85, 402, 1885, 9453, 48090, 251476, 1333517, 7177585, 39048327, 214523186, 1188037961, 6626311639, 37186187183, 209826251622, 1189699762371, 6774803376279, 38730124684829, 222194778028278, 1278828889503773, 7381829822338301, 42725078403203912

Offset: 1

Author

Andrew Howroyd, Dec 16 2020

Keywords

• nonn

Comments

Equivalence is up to permutation of the colors.

Examples

			a(1) = 1: 1.
a(2) = 2: (11), (12).
a(3) = 5: (111), (112), (1(11)), (1(12)), (1(22)).
		

Crossrefs

The case that colors may not be interchanged is A050381.

Cf. A000669, A339645, A339647.

Programs

PARI

\\ See A339645 for cycleIndexSeries and InequivalentColoringsSeq.
InequivalentColoringsSeq(cycleIndexSeries(20),2)

Formula

a(n) = A339647(n) - A000669(n).