A346226 Number of n-step 5-dimensional nonnegative lattice walks starting at the origin and using steps that increment all components or decrement one component by 1.

1, 1, 6, 31, 146, 686, 3476, 18711, 101106, 540986, 2914396, 15949626, 88494316, 493812436, 2757957496, 15432771991, 86805867666, 490992405026, 2788039913036, 15864244837646, 90398688107076, 516136925025356, 2954961007771656, 16960102805812986

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..125

Formula

a(n) == 1 (mod 5).

Maple

b:= proc(n, l) option remember; `if`(n=0, 1, (k-> `if`(n>min(l),
      add(`if`(l[i]=0, 0, b(n-1, sort(subsop(i=l[i]-1, l)))),
        i=1..k)+b(n-1, map(x-> x+1, l)), (k+1)^n))(nops(l)))
    end:
a:= n-> b(n, [0$5]):
seq(a(n), n=0..27);

Crossrefs

Column k=5 of A335570.

Sequence in context: A099621 A291002 A268401 * A240879 A056015 A128740

Adjacent sequences: A346223 A346224 A346225 * A346227 A346228 A346229

Keyword

nonn,walk

Author

Alois P. Heinz, Jul 11 2021

Status

approved