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A346230 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.

%I A346230 #7 Jul 12 2021 20:07:57
%S A346230 1,1,10,91,766,6130,48628,399403,3459646,31119382,283230172,
%T A346230 2571653926,23283756892,211338730900,1932349078216,17832773405035,
%U A346230 165944764694782,1552985405704558,14576920303430476,137021547292573186,1289614077968369716,12160967374482417964
%N A346230 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 A346230 Alois P. Heinz, <a href="/A346230/b346230.txt">Table of n, a(n) for n = 0..75</a>
%F A346230 a(n) == 1 (mod 9).
%p A346230 b:= proc(n, l) option remember; `if`(n=0, 1, (k-> `if`(n>min(l),
%p A346230       add(`if`(l[i]=0, 0, b(n-1, sort(subsop(i=l[i]-1, l)))),
%p A346230         i=1..k)+b(n-1, map(x-> x+1, l)), (k+1)^n))(nops(l)))
%p A346230     end:
%p A346230 a:= n-> b(n, [0$9]):
%p A346230 seq(a(n), n=0..27);
%Y A346230 Column k=9 of A335570.
%K A346230 nonn,walk
%O A346230 0,3
%A A346230 _Alois P. Heinz_, Jul 11 2021