A064060 Number of connected, homeomorphically irreducible (also called series-reduced) trees with n >= 2 labeled leaves (numbers in nondecreasing order).

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

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 A370258 A134991

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