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A347810
Number of n-dimensional lattice walks from {n}^n to {0}^n using steps that decrease the Euclidean distance to the origin and that change each coordinate by at most 1.
2
1, 1, 25, 2062017739, 255053951339165796439851848897794625
OFFSET
0,3
COMMENTS
Lattice points may have negative coordinates, and different walks may differ in length. All walks are self-avoiding.
LINKS
MAPLE
s:= proc(n) option remember;
`if`(n=0, [[]], map(x-> seq([x[], i], i=-1..1), s(n-1)))
end:
b:= proc(l) option remember; (n-> `if`(l=[0$n], 1, add((h-> `if`(
add(i^2, i=h)<add(i^2, i=l), b(sort(h)), 0))(l+x), x=s(n))))(nops(l))
end:
a:= n-> b([n$n]):
seq(a(n), n=0..5);
MATHEMATICA
s[n_] := s[n] = If[n == 0, {{}}, Sequence @@ Table[Append[#, i], {i, -1, 1}]& /@ s[n-1]];
b[l_List] := b[l] = With[{n = Length[l]}, If[l == Table[0, {n}], 1, Sum[With[{h = l+x}, If[h.h < l.l, b[Sort[h]], 0]], {x, s[n]}]]];
a[n_] := b[Table[n, {n}]];
Table[a[n], {n, 0, 5}] (* Jean-François Alcover, Nov 04 2021, after Alois P. Heinz *)
CROSSREFS
Main diagonal of A347811.
Cf. A034841.
Sequence in context: A191559 A279039 A237522 * A116197 A023924 A022066
KEYWORD
nonn,walk
AUTHOR
Alois P. Heinz, Sep 14 2021
STATUS
approved