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 A297567 Number of nonisomorphic proper colorings of partition star graph using three colors. 8
 3, 6, 9, 12, 12, 24, 24, 15, 36, 30, 48, 48, 18, 48, 60, 72, 96, 96, 96, 21, 60, 90, 60, 96, 192, 108, 144, 192, 192, 192, 24, 72, 120, 120, 120, 288, 240, 216, 192, 384, 384, 288, 384, 384, 384, 27, 84, 150, 180, 105, 144, 384, 480, 324, 432, 240, 576, 480, 768, 408, 384, 768, 768, 576, 768, 768, 768, 30, 96, 180, 240, 210, 168, 480, 720, 480, 432, 864, 360, 288, 768, 960, 1152, 1536, 816, 480, 1152, 960, 1536, 1536, 768 (list; graph; refs; listen; history; text; internal format)
 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=3. EXAMPLE Rows are:    3;    6;    9, 12;   12, 24, 24;   15, 36, 30, 48, 48;   18, 48, 60, 72, 96, 96, 96; MAPLE b:= (n, i)-> `if`(n=0, [3], `if`(i<1, [], [seq(map(x-> x*      binomial(2^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, {3}, If[i<1, {}, Table[Map[Function[x, x*Binomial[ 2^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 Cf. A297568, A297569, A297570. Row sums give 3*A034899. Row lengths give A000041. Sequence in context: A122809 A066662 A329517 * A285402 A153403 A336341 Adjacent sequences:  A297564 A297565 A297566 * A297568 A297569 A297570 KEYWORD nonn,tabf AUTHOR Marko Riedel, Dec 31 2017 STATUS approved

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Last modified August 15 00:08 EDT 2022. Contains 356122 sequences. (Running on oeis4.)