A359064 a(n) is the number of trees of order n such that the number of eigenvalues of the Laplacian matrix in the interval [0, 1) is equal to ceiling((d + 1)/3) = A008620(d), where d is the diameter of the tree.

2, 5, 7, 12, 20, 33, 52, 86, 137, 222, 353, 568, 900, 1433, 2260, 3574

Offset

5,1

Links

Table of n, a(n) for n=5..20.

Jiaxin Guo, Jie Xue, and Ruifang Liu, Laplacian eigenvalue distribution, diameter and domination number of trees, arXiv:2212.05283 [math.CO], 2022.

Formula

Conjecture from Guo et al.: lim_{n->oo} a(n)/A000055(n) = 0.

Crossrefs

Cf. A000055, A008620.

Sequence in context: A331529 A042065 A041793 * A333068 A029938 A213044

Adjacent sequences: A359061 A359062 A359063 * A359065 A359066 A359067

Keyword

nonn,more

Author

Stefano Spezia, Dec 15 2022

Status

approved