A034006 Number of n-step self-avoiding walks on the 4-dimensional hypercubic lattice with no non-contiguous adjacencies.

1, 8, 56, 344, 2120, 12872, 78392, 472952, 2861768, 17223224, 103835096, 623927912, 3753164744, 22526613176, 135308002424, 811435356200, 4868892591752

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• walk
• more

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=4). 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), while for d=3, we have C(n,0) = A174319(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, p. 1088 (the case d=4).

Crossrefs

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

Formula

a(n) = 8 + 48*A038746(n) + 192*A038748(n) + 384*A323037(n). (It can be proved using Eq. (5) in Nemirovsky et al. (1992).) - Petros Hadjicostas, Jan 02 2019

Extensions

Name edited by Petros Hadjicostas, Jan 01 2019

Title clarified, a(0), and a(12)-a(16) from Sean A. Irvine, Jul 29 2020