

A000644


Loops of length 4n on square grid that turn at each step and return to start in original direction.


1



1, 1, 3, 7, 31, 138, 808, 4956, 33047, 227328, 1614793, 11710299, 86495618, 648399937, 4923728056
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OFFSET

1,3


COMMENTS

Loops cannot overlap and rotations and reflections of a given loop are not counted.  Sean A. Irvine, Oct 18 2015


REFERENCES

D. E. Knuth, The Texbook, p. 390.
D. E. Knuth, personal communication.


LINKS

Table of n, a(n) for n=1..15.
Bert Dobbelaere, Illustration of initial terms
Douglas A. Torrance, Enumeration of planar Tangles, arXiv:1906.01541 [math.CO], 2019.


CROSSREFS

Sequence in context: A123488 A121620 A042271 * A015459 A115083 A141385
Adjacent sequences: A000641 A000642 A000643 * A000645 A000646 A000647


KEYWORD

nonn,more,nice,walk


AUTHOR

N. J. A. Sloane.


EXTENSIONS

a(11) from Sean A. Irvine, Oct 18 2015
Offset corrected and a(12)a(15) from Bert Dobbelaere, Jan 11 2020


STATUS

approved



