A284416


Number of selfavoiding 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 selfavoiding 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/Selfavoiding_walk">Selfavoiding walk</a>
%F a(n) = A284414(n,2n).
%Y Cf. A284414.
%K nonn,walk
%O 0,4
%A _Alois P. Heinz_, Mar 26 2017
