A034010 Number of 2n-step self avoiding closed walks on square grid, restricted to a quadrant and passing through origin.

0, 1, 2, 6, 20, 74, 300, 1302, 5944, 28266, 139010, 703102, 3641956, 19255106, 103630920, 566522778, 3140130354, 17620845976, 99977635264, 572935630884, 3313078283974

Offset

1,3

Links

Table of n, a(n) for n=1..21.

B. Hayes, How to avoid yourself, American Scientist, Vol. 86, Number 4, Jul-August 1998. p. 314-319.

Example

When the number of steps is 8, one of the six closed paths is
0___.
| ._|
|_|

Crossrefs

A subset of the polyominoes with perimeter 2n (A006725), also a subset of A002931. Cf. A000105, A038373.

Sequence in context: A188144 A245734 A150158 * A135588 A318402 A293492

Adjacent sequences: A034007 A034008 A034009 * A034011 A034012 A034013

Keyword

nonn,hard,walk

Author

Felice Russo

Extensions

Corrected and extended by David W. Wilson

a(16)-a(18) from Alex Chernov, Jan 22 2012

a(19)-a(21) from Bert Dobbelaere, Jan 06 2019

Status

approved