A038729 Configurations of linear chains in a 6-dimensional hypercubic lattice.

12, 132, 1332, 13452, 134892, 1353732, 13536612, 135457932, 1352852292, 13517235732, 134908128732, 1346796414252, 13435850843172

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=0 (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,0) = A173380(n); for d=3, we have C(n,0) = A174319(n); for d=4, we have C(n,0) = A034006(n); and for d=5, we have C(n,0) = A038726(n).) - Petros Hadjicostas, Jan 03 2019

Links

• M. E. Fisher and B. J. Hiley, Configuration and free energy of a polymer molecule with solvent interaction, J. Chem. Phys., 34 (1961), 1253-1267.
• 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 Table 1 (p. 1090).

Crossrefs

Cf. A002932, A002934, A034006, A038726, A173380, A174313, A174319.

Extensions

Terms a(10) and a(11) were copied from Table 1 (p. 1090) in the paper by Nemirovsky et al. (1992) by Petros Hadjicostas, Jan 03 2019

Name edited by Petros Hadjicostas, Jan 03 2019

a(12)-a(13) from Sean A. Irvine, Feb 01 2021