This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A038747 #43 Jul 04 2020 00:05:06
%S A038747 0,0,1,4,11,32,92,254,672,1778,4622,11938,30442,77396,194896,489620,
%T A038747 1221134,3040194,7524933,18600478,45756483,112444948,275204606,
%U A038747 673031750,1640168584,3994716336,9699476314
%N A038747 Coefficients arising in the enumeration of configurations of linear chains.
%C A038747 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=2. These numbers are given in Table II (p. 1093) in the paper. This sequence can be used for the calculation of sequence A033155(n) via Eq. (5) in the paper by Nemirovsky et al. (1992). (Note that, by equations (7b) in the paper, p_{n,1}^{(1)} = 0 for all n >= 1.) - _Petros Hadjicostas_, Jan 03 2019
%C A038747 In Table B1 (pp. 4738-4739), Bennett-Wood et al. (1998) tabulated c_n(k)/4, for various values of n and k, where c_n(k) is "the number of SAWs of length n with k nearest-neighbour contacts". (Here, the letter k stands for the letter m in the previous paragraph.) Bennett-Wood et al. (1998) worked only with a square lattice (i.e., d=2) unlike Nemirovsky et al. (1992) who worked with a d-dimensional hypercubic lattice. Both papers deal with SAWs = self-avoiding walks (in a lattice). We have c_n(k=1) = A033155(n) = 8*p_{n,1}^{(2)}, i.e., a(n) = p_{n,1}^{(2)} = (c_n(k=1)/4)/2, and this is the reason the numbers in Table B1 in Bennett-Wood et al. (1998) must be divided by 2 in order to get extra terms for the current sequence (a(12) to a(24)). - _Petros Hadjicostas_, Jan 05 2019
%H A038747 D. Bennett-Wood, I. G. Enting, D. S. Gaunt, A. J. Guttmann, J. L. Leask, A. L. Owczarek, and S. G. Whittington, <a href="https://doi.org/10.1088/0305-4470/31/20/010">Exact enumeration study of free energies of interacting polygons and walks in two dimensions</a>, J. Phys. A: Math. Gen. 31 (1998), 4725-4741.
%H A038747 M. E. Fisher and B. J. Hiley, <a href="http://dx.doi.org/10.1063/1.1731729">Configuration and free energy of a polymer molecule with solvent interaction</a>, J. Chem. Phys., 34 (1961), 1253-1267.
%H A038747 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 A038747 Cf. A033155, A038749, A047057.
%K A038747 nonn,more
%O A038747 1,4
%A A038747 _N. J. A. Sloane_, May 02 2000
%E A038747 The first two 0's in the sequence were inserted by _Petros Hadjicostas_, Jan 03 2019 to make it agree with Table II (p. 1093) and Eq. (5) (p. 1090) in the paper by Nemirovsky et al. (1992)
%E A038747 Terms a(12) to a(24) were copied from Table II, p. 4738, in the paper by Bennett-Wood et al. (1998) (after division by 2) by _Petros Hadjicostas_, Jan 05 2019
%E A038747 a(25)-a(27) from _Sean A. Irvine_, Jul 03 2020