A284231 - OEIS

%I #14 Apr 24 2017 11:45:43

%S 1,5,21,152,975,8835,75499,830180,8819417,114384573,1450018173,

%T 21689509992,319180726887,5411092531323,90615453774771,

%U 1717272516535812,32234085990345105,675335923050095253,14040521125141683717,322252846702242056280,7349647183279936080543

%N 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 Alois P. Heinz, <a href="/A284231/b284231.txt">Table of n, a(n) for n = 0..446</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_{k=n..n*(n+3)/2} (k+1) * A284414(n,k).

%e a(0) = 1: [(0,0)].

%e a(1) = 5: [(0,0),(1,0)], [(0,0),(0,1),(1,0)].

%e 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 Cf. A277424, A284230, A284414, A285673.

%K nonn,walk

%O 0,2

%A _Alois P. Heinz_, Mar 23 2017