

A010567


2nstep 3dimensional closed paths on cubic lattice.


0




OFFSET

1,1


COMMENTS

This sequence counts selfavoiding closed paths and agrees with A001413 except for n=1, for which the given value is "purely conventional" (although the convention is nonstandard): it counts 6 twostep closed paths, all of which visit no node twice but use an edge twice, so whether they are "selfavoiding" is indeed a matter of agreement. Same considerations apply to the first terms of A010568A010570.  Andrey Zabolotskiy, May 29 2018


LINKS

Table of n, a(n) for n=1..10.
M. E. Fisher and D. S. Gaunt, Ising model and selfavoiding walks on hypercubical lattices and high density expansions, Phys. Rev. 133 (1964) A224A239.


CROSSREFS

Essentially the same as A001413.
Cf. A010568 (analog in 4 dimensions), A010569 (in 5D), A010570 (in 6D), A130706 (in 1D), A010566 (in 2D, different convention for n=1), A002896 (closed walks, not necessarily selfavoiding), A001412 (selfavoiding walks, not necessarily closed), A039618, A038515.
Sequence in context: A052671 A052733 A323449 * A097171 A152886 A128614
Adjacent sequences: A010564 A010565 A010566 * A010568 A010569 A010570


KEYWORD

nonn,more


AUTHOR

N. J. A. Sloane


EXTENSIONS

a(8)a(10) copied from A001413 by Andrey Zabolotskiy, May 29 2018


STATUS

approved



