A346225 Number of n-step 4-dimensional nonnegative lattice walks starting at the origin and using steps that increment all components or decrement one component by 1.

1, 1, 5, 21, 81, 325, 1433, 6473, 28741, 128457, 585837, 2711361, 12591237, 58423305, 272649261, 1281745485, 6054729657, 28656157453, 135772544321, 645415060421, 3078755726041, 14721799860429, 70493732528001, 337920205112261, 1623127315174873, 7811948782194781

Offset: 0

Author

Alois P. Heinz, Jul 11 2021

Keywords

• nonn
• walk

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..200

Crossrefs

Column k=4 of A335570.

Programs

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$4]):
seq(a(n), n=0..27);

Formula

a(n) == 1 (mod 4).