A038749 Coefficients arising in the enumeration of configurations of linear chains.

0, 0, 0, 2, 16, 96, 510, 2558, 12282, 57498, 263421, 1192480, 5330078, 23657520, 104106655, 455993276, 1984733843, 8609546380, 37164674383

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 this sequence is p_{n,m}^{(l)} with m=1 and l=3. These numbers are given in Table II (p. 1093) in the paper. This sequence can be used for the calculation of sequence A047057 via Eq. (5) in the paper by Nemirovsky et al. (1992). (Note that, by equations (7b) in the paper, p_{n,m=1}^{(1)} = 0 for all n >= 1. Also, p_{n,m=1}^{(2)} = A038747(n) for n >= 1.) - Petros Hadjicostas, Jan 04 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, A038747, A047057.

Extensions

The first three 0's in the sequence were added by Petros Hadjicostas, Jan 04 2019 to make it agree with Table II (p. 1093) and Eq. (5) (p. 1090) in the paper by Nemirovsky et al. (1992).

a(12)-a(19) from Sean A. Irvine, Feb 02 2021