

A327871


Number of 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).


2



1, 1, 3, 14, 70, 369, 2002, 11076, 62127, 352070, 2010998, 11559030, 66780155, 387444085, 2255875650, 13174629240, 77143234950, 452738296890, 2662359410158, 15683996769460, 92540962166016, 546799192200261, 3235027635603828, 19161631961190036, 113617798289197650
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OFFSET

0,3


LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1280
Alois P. Heinz, Animation of a(5) = 369 walks
Wikipedia, Lattice path
Wikipedia, Selfavoiding walk


FORMULA

a(n) ~ sqrt(5 + 1/sqrt(13)) * (70 + 26*sqrt(13))^n / (2^(3/2) * sqrt(Pi*n) * 3^(3*n + 3/2)).  Vaclav Kotesovec, Oct 12 2019


MAPLE

b:= proc(x, y, t) option remember; `if`(min(x, y)<0, 0,
`if`(max(x, y)=0, 1, b(x1, y, 1)+
`if`(t=1, b(x1, y+1, 0)+b(x+1, y1, 0), 0)))
end:
a:= n> b(n$2, 0):
seq(a(n), n=0..25);


CROSSREFS

Cf. A001006, A086246, A327872.
Sequence in context: A161939 A270598 A001579 * A006772 A320421 A009020
Adjacent sequences: A327868 A327869 A327870 * A327872 A327873 A327874


KEYWORD

nonn,walk


AUTHOR

Alois P. Heinz, Sep 28 2019


STATUS

approved



