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

0,2

Links

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

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 *)

Crossrefs

Column k=6 of A263159.

Sequence in context: A230674 A229933 A230175 * A132591 A116232 A094496

Adjacent sequences: A263161 A263162 A263163 * A263165 A263166 A263167

Keyword

nonn

Author

Alois P. Heinz, Oct 11 2015

Status

approved