A243332 Number of simple connected graphs with n nodes that are integral and triangle-free.

1, 1, 0, 1, 1, 3, 1, 3, 0, 14, 8, 18, 33, 75

Offset

1,6

Links

Table of n, a(n) for n=1..14.

Travis Hoppe and Anna Petrone, Encyclopedia of Finite Graphs

T. Hoppe and A. Petrone, Integer sequence discovery from small graphs, arXiv preprint arXiv:1408.3644, 2014

Formula

(Sage) a243332 = lambda n: sum(1 for g in graphs.nauty_geng(f'-c -t {n}') if sum(m for _,m in g.charpoly().roots(ZZ))==n) # Max Alekseyev, Jan 31 2024

Crossrefs

Cf. A064731 (integral graphs), A024607 (triangle-free graphs).

Sequence in context: A233931 A280725 A243328 * A156872 A263526 A132301

Adjacent sequences: A243329 A243330 A243331 * A243333 A243334 A243335

Keyword

nonn,more

Author

Travis Hoppe and Anna Petrone, Jun 03 2014

Extensions

a(11)-a(14) from Max Alekseyev, Feb 02 2024

Status

approved