A001666 Number of n-step self-avoiding walks on b.c.c. lattice (version 2). (Formerly M4545 N1929)

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

Offset

0,2

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.

Sequence in context: A092521 A156088 A002914 * A214942 A010556 A010575

Adjacent sequences: A001663 A001664 A001665 * A001667 A001668 A001669

Keyword

nonn,walk,nice

Author

N. J. A. Sloane

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

Status

approved