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A284416 Number of self-avoiding planar walks of length 2n starting at (0,0), ending at (n,0), remaining in the first quadrant and using steps (0,1), (1,0), (1,1), (-1,1), and (1,-1) with the restriction that (0,1) is never used below the diagonal and (1,0) is never used above the diagonal. 3

%I

%S 1,1,1,7,17,116,536,3732,21609,152225,991680,7142207,49671146,

%T 364955208,2644449147,19764753353,147264417970,1116423286310,

%U 8488332597668,65109780090520,502742629038600,3893865922507871,30436537169536769,237651376621912220

%N Number of self-avoiding planar walks of length 2n starting at (0,0), ending at (n,0), remaining in the first quadrant and using steps (0,1), (1,0), (1,1), (-1,1), and (1,-1) with the restriction that (0,1) is never used below the diagonal and (1,0) is never used above the diagonal.

%H Alois P. Heinz, <a href="/A284416/b284416.txt">Table of n, a(n) for n = 0..360</a>

%H Alois P. Heinz, <a href="/A284416/a284416.gif">Animation of a(5)=116 walks</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Lattice_path">Lattice path</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Self-avoiding_walk">Self-avoiding walk</a>

%F a(n) = A284414(n,2n).

%Y Cf. A284414.

%K nonn,walk

%O 0,4

%A _Alois P. Heinz_, Mar 26 2017

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Last modified August 12 23:19 EDT 2020. Contains 336440 sequences. (Running on oeis4.)