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A064060 Number of connected, homeomorphically irreducible (also called series-reduced) trees with n >= 2 labeled leaves (numbers in nondecreasing order). 3
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; refs; listen; history; text; internal format)
OFFSET

2,4

COMMENTS

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_{d>=3}v_{d}, i = e-n, Sum_{d>=3}d*v_{d} = 2(v-1)-n.

LINKS

Table of n, a(n) for n=2..49.

Ch. Mayer, Illustration

Index entries for sequences related to trees

EXAMPLE

Irregular array starts:

{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};

...

CROSSREFS

The row sums give A000311(n-1), n >= 2. Cf. A007827.

Sequence in context: A281000 A146154 A068438 * A176740 A134991 A212930

Adjacent sequences:  A064057 A064058 A064059 * A064061 A064062 A064063

KEYWORD

nonn,tabf

AUTHOR

Wolfdieter Lang and Christoph Mayer (Christoph.Mayer(AT)dlr.de), Sep 13 2001

STATUS

approved

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Last modified February 28 04:39 EST 2020. Contains 332321 sequences. (Running on oeis4.)