A346227 Number of n-step 6-dimensional nonnegative lattice walks starting at the origin and using steps that increment all components or decrement one component by 1.

1, 1, 7, 43, 241, 1315, 7525, 46165, 292015, 1839901, 11536747, 72847417, 466127719, 3018752041, 19678318207, 128531220955, 840554295625, 5513681844355, 36333611660245, 240480114800023, 1596692607223561, 10621894482682471, 70761572688601777, 472172623607888563

Offset: 0

Author

Alois P. Heinz, Jul 11 2021

Keywords

• nonn
• walk

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..120

Crossrefs

Column k=6 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$6]):
seq(a(n), n=0..27);

Formula

a(n) == 1 (mod 6).