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Search: id:A064060
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| A064060 |
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Number of connected, homeomorphically irreducible (also called series-reduced) trees with n >= 2 labeled leaves (numbers in non-decreasing order). |
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3
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| 1, 1, 1, 3, 1, 10, 15, 1, 10, 15, 15, 45, 60, 90, 1, 21, 35, 70, 105, 105, 105, 105, 210, 315, 420, 630, 630, 1, 28, 35, 56, 105, 168, 210, 210, 280, 280, 280, 315, 420, 420, 560, 560, 840, 840, 840, 1260, 1260
(list; graph; listen)
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OFFSET
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2,4
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COMMENT
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The number of entries of row n of this array is A007827(n), n >= 2.
With v the total number of nodes (vertices), e the number of edges (links), n >= 2 the number of edges ending in a degree 1 node (leaves), i the number of edges which end in nodes with degree >=3 (internal edges) and v_{d} the number of nodes of degree d=1,3,4,... one has: v= e+1 = n + sum(v_{d},d>=3), i= e-n, sum(d*v_{d},d>=3) = 2(v-1)-n.
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LINKS
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Index entries for sequences related to trees
Ch. Mayer, Illustration
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EXAMPLE
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{1}; {1}; {1, 3}; {1, 10, 15}; {1, 10, 15, 15, 15, 45, 60, 90}; {1, 21, 35, 70, 105, 105, 105, 105, 210, 315, 420, 630, 630}; {1, 28, 35, 56, 105, 168, 210, 210, 280, 280, 280, 315, 420, 420, 560, 560, 840, 840, 840, 1260, 1260, 1680, 1680, 1680, 1680, 2520, 2520, 2520, 2520, 3360, 5040, 5040}, ...
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CROSSREFS
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The row sums give A000311(n-1), n >= 2. Cf. A007827.
Sequence in context: A144697 A146154 A068438 this_sequence A134991 A095327 A048953
Adjacent sequences: A064057 A064058 A064059 this_sequence A064061 A064062 A064063
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KEYWORD
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nonn,tabf
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) and Christoph Mayer (Christoph.Mayer(AT)dlr.de) Sep 13 2001
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