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

0,2

Links

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

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 *)

Crossrefs

Column k=7 of A263159.

Sequence in context: A334668 A135813 A112016 * A135982 A135983 A101327

Adjacent sequences: A263162 A263163 A263164 * A263166 A263167 A263168

Keyword

nonn

Author

Alois P. Heinz, Oct 11 2015

Status

approved