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A284231 Total number of nodes summed over all self-avoiding planar walks 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.

%I A284231 #14 Apr 24 2017 11:45:43
%S A284231 1,5,21,152,975,8835,75499,830180,8819417,114384573,1450018173,
%T A284231 21689509992,319180726887,5411092531323,90615453774771,
%U A284231 1717272516535812,32234085990345105,675335923050095253,14040521125141683717,322252846702242056280,7349647183279936080543
%N A284231 Total number of nodes summed over all self-avoiding planar walks 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 A284231 Alois P. Heinz, <a href="/A284231/b284231.txt">Table of n, a(n) for n = 0..446</a>
%H A284231 Wikipedia, <a href="https://en.wikipedia.org/wiki/Lattice_path">Lattice path</a>
%H A284231 Wikipedia, <a href="https://en.wikipedia.org/wiki/Self-avoiding_walk">Self-avoiding walk</a>
%F A284231 a(n) = Sum_{k=n..n*(n+3)/2} (k+1) * A284414(n,k).
%e A284231 a(0) = 1: [(0,0)].
%e A284231 a(1) = 5: [(0,0),(1,0)], [(0,0),(0,1),(1,0)].
%e A284231 a(2) = 21: [(0,0),(1,0),(2,0)], [(0,0),(0,1),(1,0),(2,0)], [(0,0),(1,1),(2,0)], [(0,0),(0,1),(0,2),(1,1),(2,0)], [(0,0),(1,0),(0,1),(0,2),(1,1),(2,0)].
%Y A284231 Cf. A277424, A284230, A284414, A285673.
%K A284231 nonn,walk
%O A284231 0,2
%A A284231 _Alois P. Heinz_, Mar 23 2017