A346225 Number of n-step 4-dimensional nonnegative lattice walks starting at the origin and using steps that increment all components or decrement one component by 1.

1, 1, 5, 21, 81, 325, 1433, 6473, 28741, 128457, 585837, 2711361, 12591237, 58423305, 272649261, 1281745485, 6054729657, 28656157453, 135772544321, 645415060421, 3078755726041, 14721799860429, 70493732528001, 337920205112261, 1623127315174873, 7811948782194781

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..200

Formula

a(n) == 1 (mod 4).

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$4]):
seq(a(n), n=0..27);

Crossrefs

Column k=4 of A335570.

Sequence in context: A273389 A153008 A292878 * A051196 A273454 A094834

Adjacent sequences: A346222 A346223 A346224 * A346226 A346227 A346228

Keyword

nonn,walk

Author

Alois P. Heinz, Jul 11 2021

Status

approved