A263167 - OEIS

%I #10 Apr 25 2020 14:48:19

%S 1,511,7229006221,4888774762356549331,8144781718207791515101819441,

%T 20371729407721971932197861769050382551,

%U 64254115995388375135778208276014009097192012661,235485313707274694851291521951126742198585792399471283971

%N 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.

%H Alois P. Heinz, <a href="/A263167/b263167.txt">Table of n, a(n) for n = 0..15</a>

%p g():= seq(convert(n, base, 2)[1..9], n=513..1023):

%p b:= proc(l) option remember;

%p       `if`(l[1]=0, 1, add(b(sort(l-h)), h=g()))

%p     end:

%p a:= n-> b([n$9]):

%p seq(a(n), n=0..7);

%t g[] = Table[Reverse[IntegerDigits[n, 2]][[;; 9]], {n, 2^9+1, 2^10-1}];

%t b[l_] := b[l] = If[l[[1]] == 0, 1, Sum[b[Sort[l - h]], {h, g[]}]];

%t a[n_] := b[Table[n, {9}]];

%t a /@ Range[0, 7] (* _Jean-François Alcover_, Apr 25 2020, after _Alois P. Heinz_ *)

%Y Column k=9 of A263159.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Oct 11 2015