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 A033323 #38 Jul 08 2025 19:51:12
%S A033323 0,0,0,0,32,128,344,1072,3400,9832,27600,77000,211736,572560,1534512,
%T A033323 4072664,10725424,28035128,72831272,188139616,483452824,1236865976,
%U A033323 3150044696,7994665480,20209319824,50942982080
%N A033323 Configurations of linear chains in a square lattice.
%C A033323 From _Petros Hadjicostas_, Jan 03 2019: (Start)
%C A033323 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."
%C A033323 These numbers appear in Table I (p. 1088) in the paper by Nemirovsky et al. (1992).
%C A033323 (End)
%C A033323 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
%H A033323 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 A033323 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 A033323 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).
%K A033323 nonn,more
%O A033323 1,5
%A A033323 _N. J. A. Sloane_
%E A033323 Name edited by and more terms from _Petros Hadjicostas_, Jan 03 2019
%E A033323 a(20)-a(26) from _Sean A. Irvine_, Jul 03 2020