A263164 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.

1, 63, 580693, 39991899123, 4727954015135121, 716137204351882049583, 125076804896889941384267749, 23963247580553153291287896467139, 4899254403362236213345570748744318209, 1051032705565051909388116876876306460192223

Offset: 0

Author

Alois P. Heinz, Oct 11 2015

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..50

Crossrefs

Column k=6 of A263159.

Programs

Maple

g():= seq(convert(n, base, 2)[1..6], n=65..127):
b:= proc(l) option remember;
      `if`(l[1]=0, 1, add(b(sort(l-h)), h=g()))
    end:
a:= n-> b([n$6]):
seq(a(n), n=0..10);

Mathematica

g[] = Table[Reverse[IntegerDigits[n, 2]][[;; 6]], {n, 2^6 + 1, 2^7 - 1}];
b[l_] := b[l] = If[l[[1]] == 0, 1, Sum[b[Sort[l - h]], {h, g[]}]];
a[n_] := b[Table[n, {6}]];
a /@ Range[0, 10] (* Jean-François Alcover, Apr 25 2020, after Alois P. Heinz *)