A001666 Number of n-step self-avoiding walks on b.c.c. lattice (version 2).

1, 8, 56, 392, 2648, 17960, 120056, 804824, 5351720, 35652680, 236291096, 1568049560, 10368669992, 68626647608, 453032542040, 2992783648424, 19731335857592, 130161040083608, 857282278813256, 5648892048530888, 37175039569217672, 244738250638121768

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• walk
• nice

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

• Andrey Zabolotskiy, Table of n, a(n) for n = 0..28 (from Schram et al.)
• M. E. Fisher and M. F. Sykes, Excluded-volume problem and the Ising model of ferromagnetism, Phys. Rev. 114 (1959), 45-58.
• A. J. Guttmann, On the critical behavior of self-avoiding walks II, J. Phys. A 22 (1989), 2807-2813. See Table 1.
• Raoul D. Schram, Gerard T. Barkema, Rob H. Bisseling and Nathan Clisby, Exact enumeration of self-avoiding walks on BCC and FCC lattices, J. Stat. Mech. (2017) 083208; arXiv:1703.09340 [cond-mat.stat-mech], 2017. See Table I.
• M. F. Sykes, Some counting theorems in the theory of the Ising problem and the excluded volume problem, J. Math. Phys., 2 (1961), 52-62.
• M. F. Sykes et al., The asymptotic behavior of selfavoiding walks and returns on a lattice, J. Phys. A 5 (1972), 653-660.
• Index entries for sequences related to b.c.c. lattice

Crossrefs

Equals twice A002903 except for initial term.

Cf. A001336, A001412.

Extensions

a(16)-a(18) from Bert Dobbelaere, Jan 16 2019

Terms a(19) and beyond from Schram et al. added by Andrey Zabolotskiy, Feb 02 2022

Edited by N. J. A. Sloane, Oct 16 2022