A321305 Triangle T(n,f): the number of signed cubic graphs on 2n vertices with f edges of the first sign.

1, 0, 0, 0, 0, 1, 1, 2, 3, 2, 1, 1, 2, 3, 8, 16, 21, 21, 16, 8, 3, 2, 5, 14, 57, 152, 313, 474, 551, 474, 313, 152, 57, 14, 5, 19, 91, 491, 1806, 5034, 10604, 17318, 22033, 22033, 17318, 10604, 5034, 1806, 491, 91, 19, 85, 706, 4981, 23791, 84575, 229078, 487020, 825127, 1127783, 1250632, 1127783, 825127, 487020, 229078, 84575, 23791, 4981, 706, 85

Offset

0,8

Comments

These are connected, undirected, simple cubic graphs where each edge is signed as either "+" or "-". Row n has 1+3n entries, 0<=f<=3n. The column f=0 (1, 0, 1, 2, 5,...) counts the cubic graphs (A002851). The column f=1 (0, 1, 3, 14, 91, 706,...) counts the edge-rooted cubic graphs.

Links

Table of n, a(n) for n=0..69.

Formula

T(n,f) = T(n,3*n-f).

Example

The triangle starts:
0 vertices: 1
2 vertices: 0,0,0,0
4 vertices: 1,1,2,3,2,1,1
6 vertices: 2,3,8,16,21,21,16,8,3,2
8 vertices: 5,14,57,152,313,474,551,474,313,152,57,14,5
10 vertices: 19,91,491,1806,5034,10604,17318,22033,22033,17318,10604,5034,1806,491,91,19

Crossrefs

Cf. A002851 (first column), A321304 (signed vertices), A302939 (signed trees).

Sequence in context: A105734 A076839 A092542 * A339178 A026552 A333271

Adjacent sequences: A321302 A321303 A321304 * A321306 A321307 A321308

Keyword

nonn,tabf

Author

R. J. Mathar, Nov 03 2018

Status

approved