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A034010 Number of 2n-step self avoiding closed walks on square grid, restricted to a quadrant and passing through origin. 4

%I #20 Jan 06 2019 06:08:03

%S 0,1,2,6,20,74,300,1302,5944,28266,139010,703102,3641956,19255106,

%T 103630920,566522778,3140130354,17620845976,99977635264,572935630884,

%U 3313078283974

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

%H B. Hayes, <a href="https://www.jstor.org/stable/27857052">How to avoid yourself</a>, American Scientist, Vol. 86, Number 4, Jul-August 1998. p. 314-319.

%e When the number of steps is 8, one of the six closed paths is

%e 0___.

%e | ._|

%e |_|

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

%K nonn,hard,walk

%O 1,3

%A _Felice Russo_

%E Corrected and extended by _David W. Wilson_

%E a(16)-a(18) from _Alex Chernov_, Jan 22 2012

%E a(19)-a(21) from _Bert Dobbelaere_, Jan 06 2019

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Last modified June 7 12:16 EDT 2024. Contains 373173 sequences. (Running on oeis4.)