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A346229 Number of n-step 8-dimensional nonnegative lattice walks starting at the origin and using steps that increment all components or decrement one component by 1.

%I A346229 #7 Jul 12 2021 21:17:01
%S A346229 1,1,9,73,545,3881,27761,208593,1655241,13490897,110135641,895031361,
%T A346229 7279880713,59647817713,493774294393,4125976137817,34688652854097,
%U A346229 292496479087385,2469649871976929,20883345481893257,177031405058676369,1505681846157691769
%N A346229 Number of n-step 8-dimensional nonnegative lattice walks starting at the origin and using steps that increment all components or decrement one component by 1.
%H A346229 Alois P. Heinz, <a href="/A346229/b346229.txt">Table of n, a(n) for n = 0..90</a>
%F A346229 a(n) == 1 (mod 8).
%p A346229 b:= proc(n, l) option remember; `if`(n=0, 1, (k-> `if`(n>min(l),
%p A346229       add(`if`(l[i]=0, 0, b(n-1, sort(subsop(i=l[i]-1, l)))),
%p A346229         i=1..k)+b(n-1, map(x-> x+1, l)), (k+1)^n))(nops(l)))
%p A346229     end:
%p A346229 a:= n-> b(n, [0$8]):
%p A346229 seq(a(n), n=0..27);
%Y A346229 Column k=8 of A335570.
%K A346229 nonn,walk
%O A346229 0,3
%A A346229 _Alois P. Heinz_, Jul 11 2021