A346230 Number of n-step 9-dimensional nonnegative lattice walks starting at the origin and using steps that increment all components or decrement one component by 1.

1, 1, 10, 91, 766, 6130, 48628, 399403, 3459646, 31119382, 283230172, 2571653926, 23283756892, 211338730900, 1932349078216, 17832773405035, 165944764694782, 1552985405704558, 14576920303430476, 137021547292573186, 1289614077968369716, 12160967374482417964

Offset: 0

Author

Alois P. Heinz, Jul 11 2021

Keywords

• nonn
• walk

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..75

Crossrefs

Column k=9 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$9]):
seq(a(n), n=0..27);

Formula

a(n) == 1 (mod 9).