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A010567 2n-step 3-dimensional closed paths on cubic lattice. 0
6, 24, 264, 3312, 48240, 762096, 12673920, 218904768, 3891176352, 70742410800 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This sequence counts self-avoiding closed paths and agrees with A001413 except for n=1, for which the given value is "purely conventional" (although the convention is non-standard): it counts 6 two-step closed paths, all of which visit no node twice but use an edge twice, so whether they are "self-avoiding" is indeed a matter of agreement. Same considerations apply to the first terms of A010568-A010570. - 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 self-avoiding walks on hypercubical lattices and high density expansions, Phys. Rev. 133 (1964) A224-A239.

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 self-avoiding), A001412 (self-avoiding 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

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Last modified August 7 23:50 EDT 2022. Contains 355995 sequences. (Running on oeis4.)