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 A327872 Total number of nodes in all self-avoiding 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). 2
 1, 4, 21, 148, 980, 6444, 41888, 270088, 1730079, 11023480, 69930146, 441988260, 2784820519, 17499028820, 109701885600, 686313858480, 4285914086100, 26721615383496, 166361793070466, 1034375862301240, 6423778211164860, 39850734775066644, 246976735839649218 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1276 Alois P. Heinz, Animation of A327871(5) = 369 walks with a(5) = 6444 nodes Wikipedia, Lattice path Wikipedia, Self-avoiding walk FORMULA 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 MAPLE b:= proc(x, y, t) option remember; (p-> p+[0, p[1]])(`if`(        min(x, y)<0, 0, `if`(max(x, y)=0, [1, 0], b(x-1, y, 1)+       `if`(t=1, b(x-1, y+1, 0)+b(x+1, y-1, 0), 0))))     end: a:= n-> b(n\$2, 0)[2]: seq(a(n), n=0..25); MATHEMATICA b[x_, y_, t_] := b[x, y, t] = Function[p, p + {0, p[[1]]}][If[Min[x, y] < 0, {0, 0}, If[Max[x, y] == 0, {1, 0}, b[x - 1, y, 1] + If[t == 1, b[x - 1, y + 1, 0] + b[x + 1, y - 1, 0], 0]]]]; a[n_] := b[n, n, 0][[2]]; a /@ Range[0, 25] (* Jean-François Alcover, May 13 2020, after Maple *) CROSSREFS Cf. A327871. Sequence in context: A233481 A308337 A307525 * A163861 A247054 A006153 Adjacent sequences:  A327869 A327870 A327871 * A327873 A327874 A327875 KEYWORD nonn,walk AUTHOR Alois P. Heinz, Sep 28 2019 STATUS approved

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Last modified May 12 03:56 EDT 2021. Contains 343810 sequences. (Running on oeis4.)