A001667 2n-step polygons on b.c.c. lattice.

96, 1776, 43776, 1237920, 37903776, 1223681760, 41040797376, 1416762272736, 50027402384640, 1799035070369856

Offset: 2

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• walk
• more

Comments

Number of 2n-step closed self-avoiding walks starting from the origin. - Bert Dobbelaere, Jan 16 2019

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

• P. Butera and M. Comi, Enumeration of the self-avoiding polygons on a lattice by the Schwinger-Dyson equations, Annals of Combinatorics 3, 277-286 (1999); arXiv:cond-mat/9903297, 1999.
• M. E. Fisher and M. F. Sykes, Excluded-volume problem and the Ising model of ferromagnetism, Phys. Rev. 114 (1959), 45-58.
• M. F. Sykes et al., The number of self-avoiding walks on a lattice, J. Phys. A 5 (1972), 661-666.
• Index entries for sequences related to b.c.c. lattice

Crossrefs

Cf. A001666, A001413, A001337, A038515.

Extensions

a(9)-a(10) from Bert Dobbelaere, Jan 16 2019

a(11) from Butera & Comi added by Andrey Zabolotskiy, Jun 02 2022