A038726 The number of n-step self-avoiding walks in a 5-dimensional hypercubic lattice with no non-contiguous adjacencies.

1, 10, 90, 730, 5930, 47690, 384090, 3075610, 24663210, 197117210, 1576845050, 12589411530, 100567197770, 802350892730, 6403639865530

Offset: 0

Author

N. J. A. Sloane, May 02 2000

Keywords

• nonn
• more
• walk

Comments

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=5). 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." (For d=2, we have C(n,0) = A173380(n); for d=3, we have C(n,0) = A174319(n); and for d=4, we have C(n,0) = A034006(n).) - Petros Hadjicostas, Jan 02 2019

Links

• 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; see Table I and Eq. 5 on p. 1090 (the case d=5).

Crossrefs

Cf. A034006, A038746, A038748, A173380, A174319, A323037, A323063.

Formula

a(n) = 10 + 80*A038746(n) + 480*A038748(n) + 1920*A323037(n) + 3840*A323063(n). (It can be proved using Eq. (5), p. 1090, in the paper by Nemirovsky et al. (1992).) - Petros Hadjicostas, Jan 03 2019

Extensions

Name edited by Petros Hadjicostas, Jan 02 2019

Title clarified, a(0), and a(12)-a(14) from Sean A. Irvine, Jul 29 2020