A033323 Configurations of linear chains in a square lattice.

0, 0, 0, 0, 32, 128, 344, 1072, 3400, 9832, 27600, 77000, 211736, 572560, 1534512, 4072664, 10725424, 28035128, 72831272, 188139616, 483452824, 1236865976, 3150044696, 7994665480, 20209319824, 50942982080

Offset

1,5

Comments

From Petros Hadjicostas, Jan 03 2019: (Start)

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=2). 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."

These numbers appear in Table I (p. 1088) in the paper by Nemirovsky et al. (1992).

(End)

The terms a(12) to a(19) were copied from Table B1 (pp. 4738-4739) in Bennett-Wood et al. (1998). In the table, the authors actually calculate a(n)/4 = C(n, m=2)/4 for 1 <= n <= 29. (They use the notation c_n(k), where k stands for m, which equals 2 here. They call c_n(k) "the number of SAWs of length n with k nearest-neighbour contacts".) - Petros Hadjicostas, Jan 04 2019

Links

Table of n, a(n) for n=1..26.

D. Bennett-Wood, I. G. Enting, D. S. Gaunt, A. J. Guttmann, J. L. Leask, A. L. Owczarek, and S. G. Whittington, Exact enumeration study of free energies of interacting polygons and walks in two dimensions, J. Phys. A: Math. Gen. 31 (1998), 4725-4741.

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 Eq. 7b (p. 1093).

Crossrefs

Sequence in context: A247155 A239728 A244082 * A091905 A100626 A330818

Adjacent sequences: A033320 A033321 A033322 * A033324 A033325 A033326

Keyword

nonn,more

Author

N. J. A. Sloane.

Extensions

Name edited by and more terms from Petros Hadjicostas, Jan 03 2019

a(20)-a(26) from Sean A. Irvine, Jul 03 2020

Status

approved