%I
%S 1,4,21,148,980,6444,41888,270088,1730079,11023480,69930146,441988260,
%T 2784820519,17499028820,109701885600,686313858480,4285914086100,
%U 26721615383496,166361793070466,1034375862301240,6423778211164860,39850734775066644,246976735839649218
%N Total number of nodes in all selfavoiding planar walks starting at (0,0), ending at (n,n), remaining in the first quadrant and using steps (0,1), (1,1), and (1,1) with the restriction that (1,1) and (1,1) are always immediately followed by (0,1).
%H Alois P. Heinz, <a href="/A327872/b327872.txt">Table of n, a(n) for n = 0..1276</a>
%H Alois P. Heinz, <a href="/A327871/a327871.gif">Animation of A327871(5) = 369 walks with a(5) = 6444 nodes</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) ~ sqrt(113  179/sqrt(13)) * (70 + 26*sqrt(13))^n * sqrt(n) / (sqrt(Pi) * 2^(3/2) * 3^(3*n + 3/2)).  _Vaclav Kotesovec_, Oct 12 2019
%p b:= proc(x, y, t) option remember; (p> p+[0, p[1]])(`if`(
%p min(x, y)<0, 0, `if`(max(x, y)=0, [1, 0], b(x1, y, 1)+
%p `if`(t=1, b(x1, y+1, 0)+b(x+1, y1, 0), 0))))
%p end:
%p a:= n> b(n$2, 0)[2]:
%p seq(a(n), n=0..25);
%Y Cf. A327871.
%K nonn,walk
%O 0,2
%A _Alois P. Heinz_, Sep 28 2019
