cp's OEIS Frontend

A225823 Number of hopping sequences in four-colored rooted trees with n nodes, starting and ending with the same "initial state" from all of the (two-colored) rooted trees in A198760. Compared to A198761, only one node color of the initial states is mobile on the tree (Falicov-Kimball model).

%I A225823 #27 May 06 2015 09:21:30
%S A225823 1,4,54,1568,80680,6510624,761286848,121944722176,25668462562560
%N A225823 Number of hopping sequences in four-colored rooted trees with n nodes, starting and ending with the same "initial state" from all of the (two-colored) rooted trees in A198760. Compared to A198761, only one node color of the initial states is mobile on the tree (Falicov-Kimball model).
%D A225823 G. Gruber, Entwicklung einer graphbasierten Methode zur Analyse von Hüpfsequenzen auf Butcherbäumen und deren Implementierung in Haskell, Diploma thesis, Marburg, 2011
%D A225823 M. Paech, E. Kalinowski, W. Apel, G. Gruber, R. Loogen, and E. Jeckelmann, Ground-state energy and beyond: High-accuracy results for the Hubbard model on the Bethe lattice in the strong-coupling limit, DPG Spring Meeting, Berlin, TT 45.91 (2012)
%H A225823 Eva Kalinowski and Władysław Gluza, <a href="http://arxiv.org/abs/1106.4938">Evaluation of High Order Terms for the Hubbard Model in the Strong-Coupling Limit</a> arXiv:1106.4938, 2011 (Physical Review B, January 2012)
%H A225823 Martin Paech, <a href="http://edok01.tib.uni-hannover.de/edoks/e01dh15/821459422.pdf">Numerische und algebraisch-graphentheoretische Algorithmen für korrelierte Quantensysteme</a>, Dissertation, Hannover, 2015 (in German with an abstract in English).
%Y A225823 Cf. A000081, A038055, A136793, A198760, A198761.
%K A225823 nonn,more
%O A225823 2,2
%A A225823 _Eva Kalinowski_, Jul 30 2013
%E A225823 Term a(10) added by _Martin Paech_, Sep 02 2013, calculated on a HP Integrity Superdome 2-32s by courtesy of Hewlett-Packard Development Company, L.P.