A357653 Number of walks on four-dimensional lattice from (n,n,n,n) to (0,0,0,0) using steps that decrease the Euclidean distance to the origin and that change each coordinate by 1 or by -1.

1, 1, 49, 781, 221353, 28704961, 6416941789, 1600436821729, 487955996194681, 163694597214638617, 62083509504427287565, 25552605919005414839089, 11415972657891136715599597, 5444030337763685110787232601, 2758095341306366256765459135265

Offset

0,3

Comments

Lattice points may have negative coordinates, and different walks may differ in length. All walks are self-avoiding.

All terms are odd.

Links

Alois P. Heinz, Table of n, a(n) for n = 0..175

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$4]):
seq(a(n), n=0..16);

Crossrefs

Cf. A348201.

Sequence in context: A215117 A350982 A289992 * A278284 A110906 A193940

Adjacent sequences: A357650 A357651 A357652 * A357654 A357655 A357656

Keyword

nonn,walk

Author

Alois P. Heinz, Oct 07 2022

Status

approved