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%I #10 Apr 25 2020 14:48:00
%S 1,63,580693,39991899123,4727954015135121,716137204351882049583,
%T 125076804896889941384267749,23963247580553153291287896467139,
%U 4899254403362236213345570748744318209,1051032705565051909388116876876306460192223
%N Number of lattice paths starting at {n}^6 and ending when any component equals 0, using steps that decrement one or more components by one.
%H Alois P. Heinz, <a href="/A263164/b263164.txt">Table of n, a(n) for n = 0..50</a>
%p g():= seq(convert(n, base, 2)[1..6], n=65..127):
%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$6]):
%p seq(a(n), n=0..10);
%t g[] = Table[Reverse[IntegerDigits[n, 2]][[;; 6]], {n, 2^6 + 1, 2^7 - 1}];
%t b[l_] := b[l] = If[l[[1]] == 0, 1, Sum[b[Sort[l - h]], {h, g[]}]];
%t a[n_] := b[Table[n, {6}]];
%t a /@ Range[0, 10] (* _Jean-François Alcover_, Apr 25 2020, after _Alois P. Heinz_ *)
%Y Column k=6 of A263159.
%K nonn
%O 0,2
%A _Alois P. Heinz_, Oct 11 2015
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