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

1,3

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

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.

Crossrefs

Cf. A033155, A047057.

Sequence in context: A245953 A192832 A352847 * A190601 A179404 A171343

Adjacent sequences: A042946 A042947 A042948 * A042950 A042951 A042952

Keyword

nonn,more

Author

N. J. A. Sloane

Extensions

Name edited by Petros Hadjicostas, Jan 04 2019

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

Status

approved