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

0,2

Links

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

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 *)

Crossrefs

Column k=5 of A263159.

Sequence in context: A176349 A262716 A033176 * A188956 A218142 A117579

Adjacent sequences: A263160 A263161 A263162 * A263164 A263165 A263166

Keyword

nonn

Author

Alois P. Heinz, Oct 11 2015

Status

approved