cp's OEIS Frontend

A174319 Number of n-step walks on cubic lattice (no points repeated, no adjacent points unless consecutive in path).

%I A174319 #32 Jan 04 2019 04:19:22
%S A174319 1,6,30,126,534,2214,9246,38142,157974,649086,2675022,10966470,
%T A174319 45054630,184400910,755930958,3089851782,12645783414,51635728518,
%U A174319 211059485310,861083848998,3516072837894,14334995983614,58485689950254
%N A174319 Number of n-step walks on cubic lattice (no points repeated, no adjacent points unless consecutive in path).
%C A174319 Fisher and Hiley give 2674926 as their last term instead of 2675022 (see A002934).  Douglas McNeil confirms the correction on the seqfan list.
%C A174319 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=3). 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,0) = A173380(n); for d=4, we have C(n,0) = A034006(n); and for d=5, we have C(n,0) = A038726(n).) - _Petros Hadjicostas_, Jan 03 2019
%D A174319 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A174319 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A174319 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 A174319 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.
%F A174319 a(n) = 6 + 24*A038746(n) + 48*A038748(n) for n >= 1. (It follows from Eq. (5), p. 1090, in Nemirovsky et al. (1992).) - _Petros Hadjicostas_, Jan 01 2019
%Y A174319 Cf. A002934, A038746, A038748.
%K A174319 nonn,walk,nice,more
%O A174319 0,2
%A A174319 _Joseph Myers_, Nov 27 2010
%E A174319 a(16)-a(22) from _Bert Dobbelaere_, Jan 03 2019