A001665 Number of self-avoiding n-step walks on Kagome lattice. (Formerly M3445 N1399)

1, 4, 12, 32, 88, 240, 652, 1744, 4616, 12208, 32328, 85408, 224640, 589024, 1542944, 4039256, 10560552, 27567488, 71878068, 187262944, 487526944, 1268269160, 3296832292, 8564411120, 22235825104, 57701041072, 149657337872, 387978891176, 1005378745536, 2604222063144, 6743181213712, 17454178002264

Offset

0,2

Comments

Fisher and Sykes paper gives incorrect values a(12) = 224608 and a(13) = 588832. - Sean A. Irvine, Nov 11 2012

References

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=0..31.

Sven Erick Alm, Upper and lower bounds for the connective constants of self-avoiding walks on the Archimedean and Laves lattices, J. Phys. A.: Math. Gen., 38 (2005), 2055-2080. Also technical report of the same name, 2004. See Table 6, column Kagomé.

M. E. Fisher and M. F. Sykes, Excluded-volume problem and the Ising model of ferromagnetism, Phys. Rev. 114 (1959), 45-58.

Crossrefs

Sequence in context: A271898 A276178 A120369 * A066536 A265212 A295500

Adjacent sequences: A001662 A001663 A001664 * A001666 A001667 A001668

Keyword

nonn,walk,nice

Author

N. J. A. Sloane

Extensions

Corrected and extended by Sean A. Irvine, Nov 11 2012

a(28)-a(31) from Alm (2005) added by Andrey Zabolotskiy, Oct 18 2024

Status

approved