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A284418
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Number of self-avoiding planar walks of length n*(n+1)/2 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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3
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%I #12 Oct 09 2019 13:35:01
%S 1,1,1,7,10,31,69,196,451,1168,2813,7119,17618,44206,111399,277972,
%T 709411,1763795,4543873,11269489,29244239,72402587,188977618,
%U 467258134,1225383748,3026799348,7969173506,19669004793,51959167749,128161003199,339530403506
%N Number of self-avoiding planar walks of length n*(n+1)/2 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="/A284418/a284418.gif">Animation of a(6)=69 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,n*(n+1)/2).
%Y Cf. A000217, A284414.
%K nonn,walk
%O 0,4
%A _Alois P. Heinz_, Mar 26 2017
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