cp's OEIS Frontend

A298266 Number of nonisomorphic proper colorings of partition multicycle graph using six colors.

%I A298266 #10 Sep 22 2020 05:33:15
%S A298266 1,6,21,15,56,90,40,126,315,120,240,165,252,840,720,840,600,990,624,
%T A298266 462,1890,2520,680,2240,3600,820,3465,2475,3744,2635,792,3780,6720,
%U A298266 4080,5040,12600,4800,4920,9240,14850,6600,13104,9360,15810,11160,1287,6930,15120,14280,3060,10080,33600,28800,17220,12300,20790,51975,19800,39600,13695,34944,56160,24960,55335,39525,66960,48915,2002,11880,30240,38080,18360,18480,75600,100800,27200,45920,73800,11480,41580,138600,118800,138600,99000,82170,78624,196560,74880,149760,102960,147560,237150,105400,234360,167400,293490,217040
%N A298266 Number of nonisomorphic proper colorings of partition multicycle graph using six colors.
%C A298266 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).
%H A298266 Marko Riedel et al., <a href="https://math.stackexchange.com/questions/2584928/">Orbital chromatic polynomials</a>
%F A298266 For a partition lambda we have the OCP: Product_{p^v in lambda} C(Q_p(k)+v-1, v)
%F A298266 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=6.
%e A298266 Rows are:
%e A298266     1;
%e A298266     6;
%e A298266    21,  15;
%e A298266    56,  90,  40;
%e A298266   126, 315, 120, 240, 165;
%e A298266   252, 840, 720, 840, 600, 990, 624;
%Y A298266 Cf. A297567, A297568, A297569, A297570, A298263, A298264, A298265.
%K A298266 nonn,tabf
%O A298266 0,2
%A A298266 _Marko Riedel_, Jan 15 2018