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A033323 Configurations of linear chains in a square lattice. 5


%S 0,0,0,0,32,128,344,1072,3400,9832,27600,77000,211736,572560,1534512,

%T 4072664,10725424,28035128,72831272,188139616,483452824,1236865976,

%U 3150044696,7994665480,20209319824,50942982080

%N Configurations of linear chains in a square lattice.

%C From _Petros Hadjicostas_, Jan 03 2019: (Start)

%C 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 These numbers appear in Table I (p. 1088) in the paper by Nemirovsky et al. (1992).

%C (End)

%C 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 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 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 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 nonn,more

%O 1,5

%A _N. J. A. Sloane_.

%E Name edited by and more terms from _Petros Hadjicostas_, Jan 03 2019

%E a(20)-a(26) from _Sean A. Irvine_, Jul 03 2020

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