A046788 - OEIS

%I #26 Apr 24 2021 21:49:26

%S 0,0,0,0,960,11136,98256,820896,6523248,49672560,367817184,2663082864,

%T 18939278736,132735870240,918669297696

%N Configurations of linear chains in a 4-dimensional hypercubic lattice.

%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=4). 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." (Let n >= 1. For d=2, we have C(n,m=2) = A033323(n); for d=3, we have C(n,m=2) = A049230(n); and for d=5, we have C(n,m=2) = A038728(n).) - _Petros Hadjicostas_, Jan 05 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 Table 1 on p. 1088.

%F Cf. A033323, A038728, A049230.

%K nonn,more

%O 1,5

%A _N. J. A. Sloane_

%E Name edited by _Petros Hadjicostas_, Jan 05 2019

%E a(12)-a(15) from _Sean A. Irvine_, Apr 24 2021