A339647 Number of inequivalent leaf colorings of series-reduced planted trees with n leaves using exactly 2 colors.

0, 1, 3, 17, 73, 369, 1795, 9192, 47324, 249164, 1326449, 7155620, 38979373, 214304435, 1187338427, 6624057963, 37178881395, 209802434879, 1189621738769, 6774546637528, 38729276531965, 222191966031306, 1278819536137209, 7381798618249920, 42724974018583842

Offset: 1

Author

Andrew Howroyd, Dec 16 2020

Keywords

• nonn

Comments

Equivalence is up to permutation of the colors.

Examples

			a(2) = 1: (12).
a(3) = 3: (112), (1(12)), (1(22)).
a(4) = 17: (1112), (1122), (11(12)), (11(22)), (12(11)), (12(12)), (1(112)), (1(122)), (1(222)), (1(1(12))), (1(1(22))), (1(2(11))), (1(2(12))), (1(2(22))), ((11)(12)), ((11)(22)), ((12)(12)).
		

Crossrefs

The case that colors may not be interchanged is A319377.

Column 2 of A339645.

Cf. A000669, A339646.

Programs

PARI

\\ See A339647 for cycleIndexSeries and InequivalentColoringsSeq.
{ my(S=cycleIndexSeries(20)); InequivalentColoringsSeq(S,2) - InequivalentColoringsSeq(S,1) }