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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.
2

%I #7 Jul 12 2021 21:17:01

%S 1,1,9,73,545,3881,27761,208593,1655241,13490897,110135641,895031361,

%T 7279880713,59647817713,493774294393,4125976137817,34688652854097,

%U 292496479087385,2469649871976929,20883345481893257,177031405058676369,1505681846157691769

%N 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 Alois P. Heinz, <a href="/A346229/b346229.txt">Table of n, a(n) for n = 0..90</a>

%F a(n) == 1 (mod 8).

%p b:= proc(n, l) option remember; `if`(n=0, 1, (k-> `if`(n>min(l),

%p add(`if`(l[i]=0, 0, b(n-1, sort(subsop(i=l[i]-1, l)))),

%p i=1..k)+b(n-1, map(x-> x+1, l)), (k+1)^n))(nops(l)))

%p end:

%p a:= n-> b(n, [0$8]):

%p seq(a(n), n=0..27);

%Y Column k=8 of A335570.

%K nonn,walk

%O 0,3

%A _Alois P. Heinz_, Jul 11 2021