A046788 Configurations of linear chains in a 4-dimensional hypercubic lattice.

0, 0, 0, 0, 960, 11136, 98256, 820896, 6523248, 49672560, 367817184, 2663082864, 18939278736, 132735870240, 918669297696

Offset

1,5

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=2 (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." (Let n >= 1. For d=2, we have C(n,m=2) = A033323(n); for d=3, we have C(n,m=2) = A049230(n); and for d=5, we have C(n,m=2) = A038728(n).) - Petros Hadjicostas, Jan 05 2019

Links

Table of n, a(n) for n=1..15.

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 1 on p. 1088.

Formula

Cf. A033323, A038728, A049230.

Crossrefs

Sequence in context: A247723 A330496 A057666 * A206079 A203732 A157851

Adjacent sequences: A046785 A046786 A046787 * A046789 A046790 A046791

Keyword

nonn,more

Author

N. J. A. Sloane

Extensions

Name edited by Petros Hadjicostas, Jan 05 2019

a(12)-a(15) from Sean A. Irvine, Apr 24 2021

Status

approved