A346231 Number of n-step 10-dimensional nonnegative lattice walks starting at the origin and using steps that increment all components or decrement one component by 1.

1, 1, 11, 111, 1041, 9271, 81101, 725021, 6794611, 66508821, 665254791, 6674936601, 66755513931, 666897563121, 6686651885691, 67529142206631, 687755702224881, 7056692549851951, 72780288870993221, 752810967999798491, 7798329264904129201, 80874531810513679011

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=10 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$10]):
seq(a(n), n=0..27);

Formula

a(n) == 1 (mod 10).