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A321304 Triangle T(n,f): the number of bicolored cubic graphs on 2n vertices with f vertices of the first color. 2
1, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 5, 5, 5, 2, 2, 5, 10, 31, 46, 63, 46, 31, 10, 5, 19, 64, 248, 542, 931, 1052, 931, 542, 248, 64, 19, 85, 490, 2382, 7011, 15199, 23405, 27336, 23405, 15199, 7011, 2382, 490, 85 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,10

COMMENTS

These are connected, undirected, simple cubic graphs where each vertex has either the first or the second color. Row n has 2n+1 entries, 0<=f<=2n. The column f=0 (1, 0, 2, 5,...) counts the cubic graphs (A002851). The column f=1 (0, 1, 2, 10, 64, 490...) counts the rooted cubic graphs.

LINKS

Table of n, a(n) for n=0..48.

FORMULA

T(n,f) = T(n,2n-f).

EXAMPLE

The triangle starts:

0 vertices: 1

2 vertices: 0,0,0

4 vertices: 1,1,1,1,1

6 vertices: 2,2,5,5,5,2,2

8 vertices: 5,10,31,46,63,46,31,10,5

10 vertices: 19,64,248,542,931,1052,931,542,248,64,19

CROSSREFS

Cf. A002851 (first column), A294783 (bicolored trees), A321305 (signed edges).

Sequence in context: A213187 A317921 A195710 * A280511 A200997 A063960

Adjacent sequences:  A321301 A321302 A321303 * A321305 A321306 A321307

KEYWORD

nonn,tabf,more

AUTHOR

R. J. Mathar, Nov 03 2018

STATUS

approved

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Last modified April 16 03:37 EDT 2021. Contains 343030 sequences. (Running on oeis4.)