A174319 Number of n-step walks on cubic lattice (no points repeated, no adjacent points unless consecutive in path).

1, 6, 30, 126, 534, 2214, 9246, 38142, 157974, 649086, 2675022, 10966470, 45054630, 184400910, 755930958, 3089851782, 12645783414, 51635728518, 211059485310, 861083848998, 3516072837894, 14334995983614, 58485689950254

Offset: 0

Author

Joseph Myers, Nov 27 2010

Keywords

• nonn
• walk
• nice
• more

Comments

Fisher and Hiley give 2674926 as their last term instead of 2675022 (see A002934). Douglas McNeil confirms the correction on the seqfan list.

In the notation of Nemirovsky et al. (1992), a(n), the n-th term of the current sequence is C_{n,m} with m=0 (and d=3). Here, for a d-dimensional hypercubic lattice, C_{n,m} is "the number of configurations of an n-bond self-avoiding chain with m neighbor contacts." (Let n >= 1. For d=2, we have C(n,0) = A173380(n); for d=4, we have C(n,0) = A034006(n); and for d=5, we have C(n,0) = A038726(n).) - Petros Hadjicostas, Jan 03 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

• M. E. Fisher and B. J. Hiley, Configuration and free energy of a polymer molecule with solvent interaction, J. Chem. Phys., 34 (1961), 1253-1267.
• A. M. Nemirovsky, K. F. Freed, T. Ishinabe, and J. F. Douglas, Marriage of exact enumeration and 1/d expansion methods: lattice model of dilute polymers, J. Statist. Phys., 67 (1992), 1083-1108.

Crossrefs

Cf. A002934, A038746, A038748.

Formula

a(n) = 6 + 24*A038746(n) + 48*A038748(n) for n >= 1. (It follows from Eq. (5), p. 1090, in Nemirovsky et al. (1992).) - Petros Hadjicostas, Jan 01 2019

Extensions

a(16)-a(22) from Bert Dobbelaere, Jan 03 2019