A038745 Configurations of linear chains in a 6-dimensional hypercubic lattice.

0, 0, 120, 2400, 33960, 441600, 5436960, 64509840, 745845120, 8461348080, 94558053840, 1044594244080, 11426874632880

Offset: 1

Author

N. J. A. Sloane, May 02 2000

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=6). 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); for d=3, we have C_{n, m=1} = A047057(n); for d=4, we have C_{n,m=1} = A042949(n); and for d=5, we have C_{n,m=1} = A038727(n). These values appear in Table 1, pp. 1088-1090, of Nemirovsky et al. (1992).) - Petros Hadjicostas, Jan 06 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 Eq. 5 (p. 1090) and Eq. 7b (p. 1093).

Crossrefs

Cf. A033155, A038727, A042949, A047057.

Extensions

a(10)-a(11) copied from Table 1, p. 1090, of Nemirovsky et al. (1992) by Petros Hadjicostas, Jan 06 2019

Name edited by Petros Hadjicostas, Jan 06 2019

a(12)-a(13) from Sean A. Irvine, Jan 31 2021