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A346226 Number of n-step 5-dimensional nonnegative lattice walks starting at the origin and using steps that increment all components or decrement one component by 1.

%I A346226 #7 Jul 12 2021 15:25:20
%S A346226 1,1,6,31,146,686,3476,18711,101106,540986,2914396,15949626,88494316,
%T A346226 493812436,2757957496,15432771991,86805867666,490992405026,
%U A346226 2788039913036,15864244837646,90398688107076,516136925025356,2954961007771656,16960102805812986
%N A346226 Number of n-step 5-dimensional nonnegative lattice walks starting at the origin and using steps that increment all components or decrement one component by 1.
%H A346226 Alois P. Heinz, <a href="/A346226/b346226.txt">Table of n, a(n) for n = 0..125</a>
%F A346226 a(n) == 1 (mod 5).
%p A346226 b:= proc(n, l) option remember; `if`(n=0, 1, (k-> `if`(n>min(l),
%p A346226       add(`if`(l[i]=0, 0, b(n-1, sort(subsop(i=l[i]-1, l)))),
%p A346226         i=1..k)+b(n-1, map(x-> x+1, l)), (k+1)^n))(nops(l)))
%p A346226     end:
%p A346226 a:= n-> b(n, [0$5]):
%p A346226 seq(a(n), n=0..27);
%Y A346226 Column k=5 of A335570.
%K A346226 nonn,walk
%O A346226 0,3
%A A346226 _Alois P. Heinz_, Jul 11 2021