A323063 Coefficients arising in the enumeration of configurations of linear chains.

0, 0, 0, 0, 1, 21, 282, 3102, 30583, 282368, 2494567

Offset: 1

Author

Petros Hadjicostas, Jan 03 2019

Keywords

• nonn
• more

Comments

In the notation of Nemirovsky et al. (1992), a(n), the n-th term of the current sequence, is equal to p_{n,m}^{(l)} with m = 0 and l = 5.

For a possible interpretation of this sequence (in the context of a 5-dimensional hypercubic lattice), see the comments by Bert Dobbelaere for the sequence A038748 about a cubic lattice.

We have p_{n,0}^{(2)} = A038746(n), p_{n,0}^{(3)} = A038748(n), and p_{n,0}^{(4)} = A323037(n). For p_{n,0}^{(l)} for l = 6..10, see Table II (p. 1094) in the paper by Nemirovsky et al. (1992).

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).

Crossrefs

Cf. A038726, A038729, A038746, A038748, A323037.