A346228 Number of n-step 7-dimensional nonnegative lattice walks starting at the origin and using steps that increment all components or decrement one component by 1.

1, 1, 8, 57, 372, 2332, 14960, 102173, 732124, 5306652, 38253888, 275352960, 1996376544, 14642264736, 108536296800, 809764874325, 6057499056204, 45368515203628, 340472040666080, 2563725956556584, 19381407270110656, 147036877912623840, 1118355187220657856

Offset

0,3

Links

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

Formula

a(n) == 1 (mod 7).

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$7]):
seq(a(n), n=0..27);

Crossrefs

Column k=7 of A335570.

Sequence in context: A282394 A244201 A079926 * A283125 A108666 A295711

Adjacent sequences: A346225 A346226 A346227 * A346229 A346230 A346231

Keyword

nonn,walk

Author

Alois P. Heinz, Jul 11 2021

Status

approved