A263163 Number of lattice paths starting at {n}^5 and ending when any component equals 0, using steps that decrement one or more components by one.

1, 31, 32461, 142090291, 944362553521, 7622403922836151, 68836844233002312181, 668865316589763487491811, 6842570537592835194176298241, 72725938463068824904583496062671, 796079042828286992045143086504942301, 8920612967950147759634381671622287341331

Offset: 0

Author

Alois P. Heinz, Oct 11 2015

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..75

Crossrefs

Column k=5 of A263159.

Programs

Maple

g():= seq(convert(n, base, 2)[1..5], n=33..63):
b:= proc(l) option remember;
      `if`(l[1]=0, 1, add(b(sort(l-h)), h=g()))
    end:
a:= n-> b([n$5]):
seq(a(n), n=0..12);

Mathematica

g[] = Table[Reverse[IntegerDigits[n, 2]][[;; 5]], {n, 2^5 + 1, 2^6 - 1}];
b[l_] := b[l] = If[l[[1]] == 0, 1, Sum[b[Sort[l - h]], {h, g[]}]];
a[n_] := b[Table[n, {5}]];
a /@ Range[0, 12] (* Jean-François Alcover, Apr 25 2020, after Alois P. Heinz *)