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A046342 Number of 3-bead necklaces where each bead is a planted trivalent plane tree [or anything else enumerated by the Catalan numbers], by total number of nodes. 1
1, 1, 3, 8, 24, 74, 245, 815, 2796, 9707, 34186, 121562, 436298, 1577310, 5740299, 21008777, 77279892, 285544700, 1059332082, 3944254118, 14734260864, 55207053787, 207421476390, 781283558998, 2949675307082, 11160264942376 (list; graph; refs; listen; history; internal format)
OFFSET

0,3

FORMULA

Plug g.f. for A000108, 1/2*(1-(1-4*x)^(1/2))/x, into cycle index for dihedral group D_6.

Cycle index for D_6: 1/6*Z[1]^3+1/2*Z[1]*Z[2]+1/3*Z[3].

CROSSREFS

See A058855 (a 6-bead analogue) for details.

Cf. A000108, A058855, A056711.

Sequence in context: A178543 A046919 A188175 * A000958 A148782 A148783

Adjacent sequences:  A046339 A046340 A046341 * A046343 A046344 A046345

KEYWORD

nonn

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com), Jan 19 2001

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Last modified February 17 07:30 EST 2012. Contains 205998 sequences.