A346230 - OEIS

%I #7 Jul 12 2021 20:07:57

%S 1,1,10,91,766,6130,48628,399403,3459646,31119382,283230172,

%T 2571653926,23283756892,211338730900,1932349078216,17832773405035,

%U 165944764694782,1552985405704558,14576920303430476,137021547292573186,1289614077968369716,12160967374482417964

%N 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.

%H Alois P. Heinz, <a href="/A346230/b346230.txt">Table of n, a(n) for n = 0..75</a>

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

%p b:= proc(n, l) option remember; `if`(n=0, 1, (k-> `if`(n>min(l),

%p       add(`if`(l[i]=0, 0, b(n-1, sort(subsop(i=l[i]-1, l)))),

%p         i=1..k)+b(n-1, map(x-> x+1, l)), (k+1)^n))(nops(l)))

%p     end:

%p a:= n-> b(n, [0$9]):

%p seq(a(n), n=0..27);

%Y Column k=9 of A335570.

%K nonn,walk

%O 0,3

%A _Alois P. Heinz_, Jul 11 2021