A198761 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. See comments.

2, 20, 648, 45472, 5644880, 1099056000, 310007943616, 119777421416192

Offset: 2

Author

N. J. A. Sloane, Oct 29 2011

Keywords

• nonn
• more

Comments

Compared to A225823, both node colors of the initial states are mobile on the tree (Hubbard model). - Eva Kalinowski, Jul 30 2013

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, A225823.

Extensions

Terms a(8) and a(9) added by Martin Paech, Apr 16 2012