A263166 Number of lattice paths starting at {n}^8 and ending when any component equals 0, using steps that decrement one or more components by one.

1, 255, 277284181, 7671206130046515, 463841686707958609540881, 39946850792952097272345707272335, 4211153593189257990239568354710957472133, 506051495006579137756029271328016744207715324419, 66656513992169790340795231563272399566454175106315563265

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=8 of A263159.

Programs

Maple

g():= seq(convert(n, base, 2)[1..8], n=257..511):
b:= proc(l) option remember;
      `if`(l[1]=0, 1, add(b(sort(l-h)), h=g()))
    end:
a:= n-> b([n$8]):
seq(a(n), n=0..8);

Mathematica

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