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A058855
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Number of 6-bead necklaces where each bead is an unlabeled rooted tree, by total number of nodes.
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3
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1, 1, 4, 8, 22, 52, 142, 362, 973, 2574, 6935, 18643, 50573, 137401, 375306, 1027898, 2825831, 7790055, 21539352, 59706865, 165921896, 462127857, 1289901083, 3607567539, 10108555623, 28374358327, 79777757405, 224653284863
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| The 6 beads are just place holders; only tree nodes are counted.
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FORMULA
| Plug g.f. for A000081, 1+x+x^2+2*x^3+4*x^4+ ... into cycle index for dihedral group D_12.
Cycle index for D_12 is 1/12*Z[1]^6+1/6*Z[6]+1/4*Z[1]^2*Z[2]^2+1/6*Z[3]^2+1/3*Z[2]^3.
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EXAMPLE
| a(3) = 8 since the 3 nodes may be arranged around the necklace as 111000, 110100, 101010, 210000, 201000, 200100, 300000 and in the latter arrangement there are two possible trees that can be used because A000081(3)=2.
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CROSSREFS
| Sequence in context: A000639 A190795 A052528 * A057583 A129788 A170938
Adjacent sequences: A058852 A058853 A058854 * A058856 A058857 A058858
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jan 18 2001
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