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

2,1

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

Table of n, a(n) for n=2..9.

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.

Sequence in context: A012495 A168480 A364886 * A171799 A251183 A158268

Adjacent sequences: A198758 A198759 A198760 * A198762 A198763 A198764

Keyword

nonn,more

Author

N. J. A. Sloane, Oct 29 2011

Extensions

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

Status

approved