A346229 Number of n-step 8-dimensional nonnegative lattice walks starting at the origin and using steps that increment all components or decrement one component by 1.

1, 1, 9, 73, 545, 3881, 27761, 208593, 1655241, 13490897, 110135641, 895031361, 7279880713, 59647817713, 493774294393, 4125976137817, 34688652854097, 292496479087385, 2469649871976929, 20883345481893257, 177031405058676369, 1505681846157691769

Offset

0,3

Links

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

Formula

a(n) == 1 (mod 8).

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$8]):
seq(a(n), n=0..27);

Crossrefs

Column k=8 of A335570.

Sequence in context: A244202 A079927 A126641 * A081627 A164588 A023001

Adjacent sequences: A346226 A346227 A346228 * A346230 A346231 A346232

Keyword

nonn,walk

Author

Alois P. Heinz, Jul 11 2021

Status

approved