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A298265 Number of nonisomorphic proper colorings of partition multicycle graph using five colors. 3
1, 5, 15, 10, 35, 50, 20, 70, 150, 55, 100, 70, 126, 350, 275, 300, 200, 350, 204, 210, 700, 825, 220, 700, 1000, 210, 1050, 700, 1020, 700, 330, 1260, 1925, 1100, 1400, 3000, 1100, 1050, 2450, 3500, 1400, 3060, 2040, 3500, 2340, 495, 2100, 3850, 3300, 715, 2520, 7000, 5500, 3150, 2100, 4900, 10500, 3850, 7000, 2485, 7140, 10200, 4080, 10500, 7000, 11700, 8230, 715, 3300, 6930, 7700, 3575, 4200, 14000, 16500, 4400, 7350, 10500, 1540, 8820, 24500, 19250, 21000, 14000, 12425, 14280, 30600, 11220, 20400, 14280, 24500, 35000, 14000, 35100, 23400, 41150, 29140 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A partition multicycle graph consists of a multiset of cycles with lengths given by the elements of the partition where degenerate cycles on one node are taken to be singletons and on two nodes a pair of nodes connected by an edge. 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 multicycle graph corresponding to the partition, consisting of permutations of cycles of the same length combined with rotations of individual cycles (no dihedral symmetry).

LINKS

Table of n, a(n) for n=0..96.

Marko Riedel et al., Orbital chromatic polynomials

FORMULA

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

where Q_1(k) = k, Q_2(k) = k(k-1)/2 and for n>=3, Q_n(k) = (1/n) * Sum_{d|n} phi(n/d) P_d(k) with P_d(k) = (k-1)^d + (-1)^d (k-1). Here we have k=5.

EXAMPLE

Rows are:

  1;

  5;

15,  10;

35,  50,  20;

70, 150,  55, 100,  70;

126, 350, 275, 300, 200, 350, 204;

CROSSREFS

Cf. A297567, A297568, A297569, A297570, A298263, A298264, A298266.

Sequence in context: A290837 A302841 A113259 * A291794 A321775 A166621

Adjacent sequences:  A298262 A298263 A298264 * A298266 A298267 A298268

KEYWORD

nonn,tabf

AUTHOR

Marko Riedel, Jan 15 2018

STATUS

approved

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Last modified August 21 23:04 EDT 2019. Contains 326169 sequences. (Running on oeis4.)