A346229 Number of n-step 8-dimensional nonnegative lattice walks starting at the origin and using steps that increment all components or decrement one component by 1.

1, 1, 9, 73, 545, 3881, 27761, 208593, 1655241, 13490897, 110135641, 895031361, 7279880713, 59647817713, 493774294393, 4125976137817, 34688652854097, 292496479087385, 2469649871976929, 20883345481893257, 177031405058676369, 1505681846157691769

Offset: 0

Author

Alois P. Heinz, Jul 11 2021

Keywords

• nonn
• walk

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..90

Crossrefs

Column k=8 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$8]):
seq(a(n), n=0..27);

Formula

a(n) == 1 (mod 8).