

A321305


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


2



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
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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 edgerooted cubic graphs.


LINKS

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


FORMULA

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


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



