A263165 Number of lattice paths starting at {n}^7 and ending when any component equals 0, using steps that decrement one or more components by one.

1, 127, 11917837, 15302345348179, 38074918201135688881, 127994492508527577494290807, 511210318493877135287739912958933, 2283244029676857615289372083169016508547, 11029283913008516141643899112236047179180872449

Offset: 0

Author

Alois P. Heinz, Oct 11 2015

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..20

Crossrefs

Column k=7 of A263159.

Programs

Maple

g():= seq(convert(n, base, 2)[1..7], n=129..255):
b:= proc(l) option remember;
      `if`(l[1]=0, 1, add(b(sort(l-h)), h=g()))
    end:
a:= n-> b([n$7]):
seq(a(n), n=0..9);

Mathematica

g[] = Table[Reverse[IntegerDigits[n, 2]][[;; 7]], {n, 2^7 + 1, 2^8 - 1}];
b[l_] := b[l] = If[l[[1]] == 0, 1, Sum[b[Sort[l - h]], {h, g[]}]];
a[n_] := b[Table[n, {7}]];
a /@ Range[0, 9] (* Jean-François Alcover, Apr 25 2020, after Alois P. Heinz *)