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A284416
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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.
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%I #15 Oct 09 2019 13:34:55
%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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