A318228 Number of inequivalent leaf-colorings of planted achiral trees with n nodes.

1, 1, 3, 6, 13, 20, 43, 58, 115, 171, 323, 379, 1034, 1135, 2321, 4327, 8915, 9212, 33939, 34429, 128414, 234017, 417721, 418976, 2931624, 5096391, 11770830, 20357876, 64853630, 64858195

Offset: 1

Author

Gus Wiseman, Aug 21 2018

Keywords

• nonn
• more

Comments

In a planted achiral tree, all branches directly under any given branch are identical.

Examples

			Inequivalent representatives of the a(5) = 13 leaf-colorings:
  (1111)  ((111))  ((1)(1))  (((11)))  ((((1))))
  (1112)  ((112))  ((1)(2))  (((12)))
  (1122)  ((123))
  (1123)
  (1234)
		

Crossrefs

Cf. A000081, A001190, A001678, A003238, A004111, A214577, A290689, A304486.

Cf. A318226, A318227, A318229, A318230, A318231, A318234, A339645.

Programs

PARI

\\ See links in A339645 for combinatorial species functions.
G(v)={my(t=2, p=sv(1)); for(i=1, #v, my(d=v[i]); if(d>1, p=sApplyCI(symGroupCycleIndex(d), d, p, t)); t=t*d+1); p}
cycleIndex(n)={my(recurse(r,v)=if(r==1, G(v), sumdiv(r-1, d, self()((r-1)/d, concat(d,v))))); recurse(n,[])}
a(n)={StructsByCycleIndex(n, cycleIndex(n), n)} \\ Andrew Howroyd, Dec 13 2020

Extensions

a(9)-a(30) from Andrew Howroyd, Dec 11 2020