A210507 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

A210507

Number of labeled graphs on [n] with unicyclic components containing a given edge.

1, 10, 111, 1468, 22940, 416250, 8626660, 201349672, 5230931454, 149783426470, 4688281021490, 159284662406460, 5838769123729984, 229711022253150382, 9655348958575618320, 431845990498159342000, 20479127764425617465660, 1026429489947790074019978

(list; graph; refs; listen; history; text; internal format)

OFFSET

3,2

COMMENTS

This gives the number of matroid bases that contain a given element (edge) of the bicircular matroid of K_n.

REFERENCES

O. Giménez, A. de Mier, M. Noy, On the Number of Bases of Bicircular Matroids, Ann. Comb. 9 (2005), no. 1, 35-45.

LINKS

Table of n, a(n) for n=3..20.

FORMULA

a(n) = 2*b(n)/(n-1), where b(n) is seq A137916.

EXAMPLE

a(4)=10 means that 10 (of the 15) labeled unicyclic graphs on 4 vertices contain a given edge.

CROSSREFS

Cf. A137916.

Sequence in context: A122574 A176736 A084031 * A066275 A362671 A344398

Adjacent sequences: A210504 A210505 A210506 * A210508 A210509 A210510

KEYWORD

nonn

AUTHOR

Gary Gordon, Jan 25 2013

STATUS

approved