

A038726


The number of nstep selfavoiding walks in a 5dimensional hypercubic lattice with no noncontiguous adjacencies.


3



1, 10, 90, 730, 5930, 47690, 384090, 3075610, 24663210, 197117210, 1576845050, 12589411530, 100567197770, 802350892730, 6403639865530
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OFFSET

0,2


COMMENTS

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=5). Here, for a ddimensional hypercubic lattice, C_{n,m} is "the number of configurations of an nbond selfavoiding 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


LINKS

Table of n, a(n) for n=0..14.
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; see Table I and Eq. 5 on p. 1090 (the case d=5).


FORMULA

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


CROSSREFS

Cf. A034006, A038746, A038748, A173380, A174319, A323037, A323063.
Sequence in context: A319874 A159733 A265325 * A009454 A231530 A242652
Adjacent sequences: A038723 A038724 A038725 * A038727 A038728 A038729


KEYWORD

nonn,more,walk


AUTHOR

N. J. A. Sloane, May 02 2000


EXTENSIONS

Name edited by Petros Hadjicostas, Jan 02 2019
Title clarified, a(0), and a(12)a(14) from Sean A. Irvine, Jul 29 2020


STATUS

approved



