

A174319


Number of nstep 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
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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 nth term of the current sequence is C_{n,m} with m=0 (and d=3). Here, for a ddimensional hypercubic lattice, C_{n,m} is "the number of configurations of an nbond selfavoiding 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

Table of n, a(n) for n=0..22.
M. E. Fisher and B. J. Hiley, Configuration and free energy of a polymer molecule with solvent interaction, J. Chem. Phys., 34 (1961), 12531267.
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), 10831108.


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



