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Number of distinct characteristic polynomials of trees with n nodes.
0

%I #34 Mar 02 2020 12:29:38

%S 1,1,1,1,2,3,6,11,22,42,102,204,488,1078,2723,6403,16479,40313,106135,

%T 271295,724455

%N Number of distinct characteristic polynomials of trees with n nodes.

%D D. M. Cvetković, M. Doob and H. Sachs, Spectra of graphs. Theory and applications, Johann Ambrosius Barth, Heidelberg, 1995.

%H M. Fürer, <a href="https://doi.org/10.1007/978-3-642-04128-0_2">Efficient computation of the characteristic polynomial of a tree and related tasks</a>. Algorithms-ESA 2009, p. 11-22.

%o (Sage) [len(Set([t.charpoly() for t in graphs.trees(n)])) for n in range(14)]

%Y Cf. A000055.

%K nonn,more

%O 0,5

%A _F. Chapoton_, Jun 13 2013

%E a(0) = 1 added by _Peter Luschny_, Mar 01 2020

%E a(17)-a(20) from _F. Chapoton_, Mar 02 2020