A263167 Number of lattice paths starting at {n}^9 and ending when any component equals 0, using steps that decrement one or more components by one.

1, 511, 7229006221, 4888774762356549331, 8144781718207791515101819441, 20371729407721971932197861769050382551, 64254115995388375135778208276014009097192012661, 235485313707274694851291521951126742198585792399471283971

Offset: 0

Author

Alois P. Heinz, Oct 11 2015

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..15

Crossrefs

Column k=9 of A263159.

Programs

Maple

g():= seq(convert(n, base, 2)[1..9], n=513..1023):
b:= proc(l) option remember;
      `if`(l[1]=0, 1, add(b(sort(l-h)), h=g()))
    end:
a:= n-> b([n$9]):
seq(a(n), n=0..7);

Mathematica

g[] = Table[Reverse[IntegerDigits[n, 2]][[;; 9]], {n, 2^9+1, 2^10-1}];
b[l_] := b[l] = If[l[[1]] == 0, 1, Sum[b[Sort[l - h]], {h, g[]}]];
a[n_] := b[Table[n, {9}]];
a /@ Range[0, 7] (* Jean-François Alcover, Apr 25 2020, after Alois P. Heinz *)