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A284428 Number of all self-avoiding planar walks of length j (0<=j<=n) starting at (0,0), ending at (n-j,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.

%I A284428 #17 Oct 09 2019 13:35:09
%S A284428 1,0,1,1,2,1,5,5,13,15,40,44,123,156,402,536,1361,1857,4689,6681,
%T A284428 16536,24286,59400,89131,216114,331324,796029,1243168,2963859,4700410,
%U A284428 11133792,17901901,42155014,68618679,160736012,264497624,616693942,1024713750,2379184108
%N A284428 Number of all self-avoiding planar walks of length j (0<=j<=n) starting at (0,0), ending at (n-j,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 A284428 Alois P. Heinz, <a href="/A284428/b284428.txt">Table of n, a(n) for n = 0..675</a>
%H A284428 Alois P. Heinz, <a href="/A284428/a284428.gif">Animation of a(12)=123 walks</a>
%H A284428 Wikipedia, <a href="https://en.wikipedia.org/wiki/Lattice_path">Lattice path</a>
%H A284428 Wikipedia, <a href="https://en.wikipedia.org/wiki/Self-avoiding_walk">Self-avoiding walk</a>
%Y A284428 Antidiagonal sums of A284414.
%K A284428 nonn,walk
%O A284428 0,5
%A A284428 _Alois P. Heinz_, Mar 26 2017