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A038096
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Number of rooted graphs where root has degree 3.
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1
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32, 1280, 61440, 4587520, 587202560, 135291469824, 57724360458240, 46443371157258240, 71337018097548656640, 211030752203237270487040, 1210134745434243803880882176, 13518305228996352601898436526080
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OFFSET
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4,1
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COMMENTS
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The graphs are not necessarily connected. The nodes are labeled.
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LINKS
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Table of n, a(n) for n=4..15.
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FORMULA
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n*C(n-1,3)*2^C(n-1,2). (There are n choices for the root, C(n-1,3) choices for the nodes it joined to, and 2^C(n-1,2) choices for the edges between the non-root nodes.)
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EXAMPLE
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For n=4, take 4 nodes labeled a,b,c,d. We can choose the root in 4 ways, say a, and it must be joined to b,c,d. Each of the three edges bc, bd, cd may or may not exist, so there are 4*8 = 32 = a(4) possibilities.
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MATHEMATICA
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Table[n Binomial[n-1, 3] 2^Binomial[n-1, 2], {n, 4, 20}] (* From Harvey P. Dale, Sep 14 2011 *)
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CROSSREFS
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Cf. A006125, A038094-A038097.
Sequence in context: A189956 A194652 A208707 * A160447 A220577 A200258
Adjacent sequences: A038093 A038094 A038095 * A038097 A038098 A038099
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KEYWORD
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nonn,easy
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AUTHOR
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Christian G. Bower, Jan 04 1999.
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EXTENSIONS
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Edited by N. J. A. Sloane, Sep 14 2011
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STATUS
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approved
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