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A346231 Number of n-step 10-dimensional nonnegative lattice walks starting at the origin and using steps that increment all components or decrement one component by 1.

%I A346231 #7 Jul 12 2021 19:34:25
%S A346231 1,1,11,111,1041,9271,81101,725021,6794611,66508821,665254791,
%T A346231 6674936601,66755513931,666897563121,6686651885691,67529142206631,
%U A346231 687755702224881,7056692549851951,72780288870993221,752810967999798491,7798329264904129201,80874531810513679011
%N A346231 Number of n-step 10-dimensional nonnegative lattice walks starting at the origin and using steps that increment all components or decrement one component by 1.
%H A346231 Alois P. Heinz, <a href="/A346231/b346231.txt">Table of n, a(n) for n = 0..75</a>
%F A346231 a(n) == 1 (mod 10).
%p A346231 b:= proc(n, l) option remember; `if`(n=0, 1, (k-> `if`(n>min(l),
%p A346231       add(`if`(l[i]=0, 0, b(n-1, sort(subsop(i=l[i]-1, l)))),
%p A346231         i=1..k)+b(n-1, map(x-> x+1, l)), (k+1)^n))(nops(l)))
%p A346231     end:
%p A346231 a:= n-> b(n, [0$10]):
%p A346231 seq(a(n), n=0..27);
%Y A346231 Column k=10 of A335570.
%K A346231 nonn,walk
%O A346231 0,3
%A A346231 _Alois P. Heinz_, Jul 11 2021