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
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=4.
EXAMPLE
Rows are:
4;
12;
24, 36;
40, 108, 108;
60, 216, 180, 324, 324;
84, 360, 540, 648, 972, 972, 972;
MAPLE
b:= (n, i)-> `if`(n=0, [4], `if`(i<1, [], [seq(map(x-> x*
binomial(3^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, {4}, If[i<1, {}, Table[Map[Function[x, x*Binomial[ 3^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-François Alcover, Jan 17 2018, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Marko Riedel, Dec 31 2017
STATUS
approved