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%I #19 Oct 09 2019 13:34:49
%S 1,1,3,5,14,34,96,259,748,2142,6329,18727,56358,170370,520354,1596980,
%T 4935307,15319460,47794472,149681904,470620062,1484513696,4697619876,
%U 14906459690,47426014833,151247657528,483426998881,1548323383749,4968516324954,15972198595374
%N Number of self-avoiding planar walks of length n starting at (0,0), ending on the x-axis, 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="/A284415/b284415.txt">Table of n, a(n) for n = 0..516</a>
%H Alois P. Heinz, <a href="/A284415/a284415.gif">Animation of a(6)=96 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) = Sum_{j=floor((sqrt(1+8*n)-1)/2)..n} A284414(j,n).
%Y Column sums of A284414.
%Y Cf. A001006, A003056.
%K nonn,walk
%O 0,3
%A _Alois P. Heinz_, Mar 26 2017