A042949 Configurations of linear chains in a 4-dimensional hypercubic lattice.

0, 0, 48, 576, 4752, 36864, 271680, 1931808, 13384320, 91133664, 610863072, 4051654752, 26592186336, 173304754368, 1121024960064

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=1 (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,m=1} = A033155(n) while for d=3, we have C_{n,m=1}=A047057(n).) These numbers are given in Table I (p. 1088) in the paper by Nemirovsky et al. (1992). - Petros Hadjicostas, Jan 04 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.

Crossrefs

Cf. A033155, A047057.

Extensions

Name edited by Petros Hadjicostas, Jan 04 2019

a(12)-a(15) from Sean A. Irvine, Jan 31 2021