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).

1, 4, 54, 1568, 80680, 6510624, 761286848, 121944722176, 25668462562560

Offset: 2

Author

Eva Kalinowski, Jul 30 2013

Keywords

• nonn
• more

References

• G. Gruber, Entwicklung einer graphbasierten Methode zur Analyse von Hüpfsequenzen auf Butcherbäumen und deren Implementierung in Haskell, Diploma thesis, Marburg, 2011
• 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)

Links

• Eva Kalinowski and Władysław Gluza, Evaluation of High Order Terms for the Hubbard Model in the Strong-Coupling Limit arXiv:1106.4938, 2011 (Physical Review B, January 2012)
• Martin Paech, Numerische und algebraisch-graphentheoretische Algorithmen für korrelierte Quantensysteme, Dissertation, Hannover, 2015 (in German with an abstract in English).

Crossrefs

Cf. A000081, A038055, A136793, A198760, A198761.

Extensions

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.