The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 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 * A309620 A291794 A321775 Adjacent sequences:  A298262 A298263 A298264 * A298266 A298267 A298268 KEYWORD nonn,tabf AUTHOR Marko Riedel, Jan 15 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 10 21:08 EDT 2021. Contains 343780 sequences. (Running on oeis4.)