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A297569 Number of nonisomorphic proper colorings of partition star graph using five colors. 7
5, 20, 50, 80, 100, 320, 320, 175, 800, 680, 1280, 1280, 280, 1600, 2720, 3200, 5120, 5120, 5120, 420, 2800, 6800, 4080, 6400, 20480, 10400, 12800, 20480, 20480, 20480, 600, 4480, 13600, 16320, 11200, 51200, 43520, 41600, 25600, 81920, 81920, 51200, 81920, 81920, 81920, 825, 6720, 23800, 40800, 19380, 17920, 102400, 174080, 104000, 166400, 44800, 204800, 174080, 327680, 164480, 102400, 327680, 327680, 204800, 327680, 327680 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

A partition star graph consists of a multiset of paths with lengths given by the elements of the partition attached to a distinguished root node. The ordering of the partitions is by traversing antichains in Young's lattice bottom to top, left to right. Isomorphism refers to the automorphisms of the star graph corresponding to the partition.

LINKS

Table of n, a(n) for n=0..65.

Marko Riedel et al., Orbital chromatic polynomials

FORMULA

For a partition lambda we have the OCP: k Product_{p^v in lambda} C((k-1)^p+v-1, v). Here we have k=5.

EXAMPLE

Rows are:

    5;

   20,

   50,   80;

  100,  320,  320;

  175,  800,  680, 1280, 1280;

  280, 1600, 2720, 3200, 5120, 5120, 5120;

MAPLE

b:= (n, i)-> `if`(n=0, [5], `if`(i<1, [], [seq(map(x-> x*

     binomial(4^i+j-1, j), b(n-i*j, i-1))[], j=0..n/i)])):

T:= n-> b(n$2)[]:

seq(T(n), n=0..10);  # Alois P. Heinz, Jan 14 2018

MATHEMATICA

b[n_, i_] := If[n == 0, {5}, If[i<1, {}, Table[Map[Function[x, x*Binomial[ 4^i + j - 1, j]], b[n - i*j, i - 1]], {j, 0, n/i}]] // Flatten];

T[n_] := b[n, n];

Table[T[n], {n, 0, 10}] // Flatten (* Jean-Fran├žois Alcover, Jan 17 2018, after Alois P. Heinz *)

CROSSREFS

Cf. A297567, A297568, A297570.

Row sums give 5*A144068.

Row lengths give A000041.

Sequence in context: A147002 A005287 A147488 * A190094 A134481 A062158

Adjacent sequences:  A297566 A297567 A297568 * A297570 A297571 A297572

KEYWORD

nonn,tabf

AUTHOR

Marko Riedel, Dec 31 2017

STATUS

approved

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Last modified October 27 20:15 EDT 2021. Contains 348290 sequences. (Running on oeis4.)