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A318228 Number of inequivalent leaf-colorings of planted achiral trees with n nodes. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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

LINKS

Table of n, a(n) for n=1..30.

EXAMPLE

Inequivalent representatives of the a(5) = 13 leaf-colorings:

  (1111)  ((111))  ((1)(1))  (((11)))  ((((1))))

  (1112)  ((112))  ((1)(2))  (((12)))

  (1122)  ((123))

  (1123)

  (1234)

PROG

(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

CROSSREFS

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

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

Sequence in context: A230370 A285246 A147009 * A064290 A064621 A330588

Adjacent sequences:  A318225 A318226 A318227 * A318229 A318230 A318231

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Aug 21 2018

EXTENSIONS

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

STATUS

approved

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Last modified September 17 06:16 EDT 2021. Contains 347478 sequences. (Running on oeis4.)