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%I #37 Jul 29 2020 15:36:21
%S 1,10,90,730,5930,47690,384090,3075610,24663210,197117210,1576845050,
%T 12589411530,100567197770,802350892730,6403639865530
%N The number of n-step self-avoiding walks in a 5-dimensional hypercubic lattice with no non-contiguous adjacencies.
%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=0 (and d=5). 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." (For d=2, we have C(n,0) = A173380(n); for d=3, we have C(n,0) = A174319(n); and for d=4, we have C(n,0) = A034006(n).) - _Petros Hadjicostas_, Jan 02 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 I and Eq. 5 on p. 1090 (the case d=5).
%F a(n) = 10 + 80*A038746(n) + 480*A038748(n) + 1920*A323037(n) + 3840*A323063(n). (It can be proved using Eq. (5), p. 1090, in the paper by Nemirovsky et al. (1992).) - _Petros Hadjicostas_, Jan 03 2019
%Y Cf. A034006, A038746, A038748, A173380, A174319, A323037, A323063.
%K nonn,more,walk
%O 0,2
%A _N. J. A. Sloane_, May 02 2000
%E Name edited by _Petros Hadjicostas_, Jan 02 2019
%E Title clarified, a(0), and a(12)-a(14) from _Sean A. Irvine_, Jul 29 2020
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