A000644 Number of loops of length 4n on square grid that turn at each step and return to start in original direction.

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

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