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 A174319 Number of n-step walks on cubic lattice (no points repeated, no adjacent points unless consecutive in path). 12
 1, 6, 30, 126, 534, 2214, 9246, 38142, 157974, 649086, 2675022, 10966470, 45054630, 184400910, 755930958, 3089851782, 12645783414, 51635728518, 211059485310, 861083848998, 3516072837894, 14334995983614, 58485689950254 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Fisher and Hiley give 2674926 as their last term instead of 2675022 (see A002934).  Douglas McNeil confirms the correction on the seqfan list. 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 REFERENCES N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS M. E. Fisher and B. J. Hiley, Configuration and free energy of a polymer molecule with solvent interaction, J. Chem. Phys., 34 (1961), 1253-1267. A. M. Nemirovsky, K. F. Freed, T. Ishinabe, and J. F. Douglas, Marriage of exact enumeration and 1/d expansion methods: lattice model of dilute polymers, J. Statist. Phys., 67 (1992), 1083-1108. FORMULA 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 CROSSREFS Cf. A002934, A038746, A038748. Sequence in context: A344344 A002446 A002934 * A337456 A334326 A131458 Adjacent sequences:  A174316 A174317 A174318 * A174320 A174321 A174322 KEYWORD nonn,walk,nice,more AUTHOR Joseph Myers, Nov 27 2010 EXTENSIONS a(16)-a(22) from Bert Dobbelaere, Jan 03 2019 STATUS approved

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Last modified September 28 04:24 EDT 2021. Contains 347698 sequences. (Running on oeis4.)