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

Author

N. J. A. Sloane

Keywords

• nonn
• 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=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

• 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.

Extensions

Name edited by Petros Hadjicostas, Jan 05 2019

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