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A346227 Number of n-step 6-dimensional nonnegative lattice walks starting at the origin and using steps that increment all components or decrement one component by 1.

%I A346227 #7 Jul 13 2021 16:02:43
%S A346227 1,1,7,43,241,1315,7525,46165,292015,1839901,11536747,72847417,
%T A346227 466127719,3018752041,19678318207,128531220955,840554295625,
%U A346227 5513681844355,36333611660245,240480114800023,1596692607223561,10621894482682471,70761572688601777,472172623607888563
%N A346227 Number of n-step 6-dimensional nonnegative lattice walks starting at the origin and using steps that increment all components or decrement one component by 1.
%H A346227 Alois P. Heinz, <a href="/A346227/b346227.txt">Table of n, a(n) for n = 0..120</a>
%F A346227 a(n) == 1 (mod 6).
%p A346227 b:= proc(n, l) option remember; `if`(n=0, 1, (k-> `if`(n>min(l),
%p A346227       add(`if`(l[i]=0, 0, b(n-1, sort(subsop(i=l[i]-1, l)))),
%p A346227         i=1..k)+b(n-1, map(x-> x+1, l)), (k+1)^n))(nops(l)))
%p A346227     end:
%p A346227 a:= n-> b(n, [0$6]):
%p A346227 seq(a(n), n=0..27);
%Y A346227 Column k=6 of A335570.
%K A346227 nonn,walk
%O A346227 0,3
%A A346227 _Alois P. Heinz_, Jul 11 2021