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

0,2

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

Table of n, a(n) for n=0..16.

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).

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

Crossrefs

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

Sequence in context: A319891 A319872 A215227 * A334333 A307813 A291387

Adjacent sequences: A034003 A034004 A034005 * A034007 A034008 A034009

Keyword

nonn,walk,more

Author

N. J. A. Sloane

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

Status

approved