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

0,3

Links

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

Formula

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

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);

Crossrefs

Column k=9 of A335570.

Sequence in context: A002739 A344389 A079928 * A231412 A002452 A096261

Adjacent sequences: A346227 A346228 A346229 * A346231 A346232 A346233

Keyword

nonn,walk

Author

Alois P. Heinz, Jul 11 2021

Status

approved