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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.

%I A346225 #7 Jul 12 2021 15:26:08
%S A346225 1,1,5,21,81,325,1433,6473,28741,128457,585837,2711361,12591237,
%T A346225 58423305,272649261,1281745485,6054729657,28656157453,135772544321,
%U A346225 645415060421,3078755726041,14721799860429,70493732528001,337920205112261,1623127315174873,7811948782194781
%N 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.
%H A346225 Alois P. Heinz, <a href="/A346225/b346225.txt">Table of n, a(n) for n = 0..200</a>
%F A346225 a(n) == 1 (mod 4).
%p A346225 b:= proc(n, l) option remember; `if`(n=0, 1, (k-> `if`(n>min(l),
%p A346225       add(`if`(l[i]=0, 0, b(n-1, sort(subsop(i=l[i]-1, l)))),
%p A346225         i=1..k)+b(n-1, map(x-> x+1, l)), (k+1)^n))(nops(l)))
%p A346225     end:
%p A346225 a:= n-> b(n, [0$4]):
%p A346225 seq(a(n), n=0..27);
%Y A346225 Column k=4 of A335570.
%K A346225 nonn,walk
%O A346225 0,3
%A A346225 _Alois P. Heinz_, Jul 11 2021