%I #10 Apr 25 2020 14:48:13

%S 1,255,277284181,7671206130046515,463841686707958609540881,

%T 39946850792952097272345707272335,

%U 4211153593189257990239568354710957472133,506051495006579137756029271328016744207715324419,66656513992169790340795231563272399566454175106315563265

%N Number of lattice paths starting at {n}^8 and ending when any component equals 0, using steps that decrement one or more components by one.

%H Alois P. Heinz, <a href="/A263166/b263166.txt">Table of n, a(n) for n = 0..20</a>

%p g():= seq(convert(n, base, 2)[1..8], n=257..511):

%p b:= proc(l) option remember;

%p `if`(l[1]=0, 1, add(b(sort(l-h)), h=g()))

%p end:

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

%p seq(a(n), n=0..8);

%t g[] = Table[Reverse[IntegerDigits[n, 2]][[;; 8]], {n, 2^8 + 1, 2^9 - 1}];

%t b[l_] := b[l] = If[l[[1]] == 0, 1, Sum[b[Sort[l - h]], {h, g[]}]];

%t a[n_] := b[Table[n, {8}]];

%t a /@ Range[0, 8] (* _Jean-François Alcover_, Apr 25 2020, after _Alois P. Heinz_ *)

%Y Column k=8 of A263159.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Oct 11 2015