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Coefficients arising in the enumeration of configurations of linear chains.
2

%I #27 Feb 02 2021 04:32:40

%S 0,0,0,2,16,96,510,2558,12282,57498,263421,1192480,5330078,23657520,

%T 104106655,455993276,1984733843,8609546380,37164674383

%N Coefficients arising in the enumeration of configurations of linear chains.

%C 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

%H A. M. Nemirovsky, K. F. Freed, T. Ishinabe, and J. F. Douglas, <a href="http://dx.doi.org/10.1007/BF01049010">Marriage of exact enumeration and 1/d expansion methods: lattice model of dilute polymers</a>, J. Statist. Phys., 67 (1992), 1083-1108; see Eq. 5 (p. 1090) and Eq. 7b (p. 1093).

%Y Cf. A033155, A038747, A047057.

%K nonn,more

%O 1,4

%A _N. J. A. Sloane_, May 02 2000

%E 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).

%E a(12)-a(19) from _Sean A. Irvine_, Feb 02 2021