cp's OEIS Frontend

A298265 Number of nonisomorphic proper colorings of partition multicycle graph using five colors.

%I A298265 #10 Sep 22 2020 05:33:07
%S A298265 1,5,15,10,35,50,20,70,150,55,100,70,126,350,275,300,200,350,204,210,
%T A298265 700,825,220,700,1000,210,1050,700,1020,700,330,1260,1925,1100,1400,
%U A298265 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
%N A298265 Number of nonisomorphic proper colorings of partition multicycle graph using five colors.
%C A298265 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 A298265 Marko Riedel et al., <a href="https://math.stackexchange.com/questions/2584928/">Orbital chromatic polynomials</a>
%F A298265 For a partition lambda we have the OCP: Product_{p^v in lambda} C(Q_p(k)+v-1, v)
%F A298265 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.
%e A298265 Rows are:
%e A298265     1;
%e A298265     5;
%e A298265    15,  10;
%e A298265    35,  50,  20;
%e A298265    70, 150,  55, 100,  70;
%e A298265   126, 350, 275, 300, 200, 350, 204;
%Y A298265 Cf. A297567, A297568, A297569, A297570, A298263, A298264, A298266.
%K A298265 nonn,tabf
%O A298265 0,2
%A A298265 _Marko Riedel_, Jan 15 2018