OFFSET
0,6
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..4179
A. M. Odlyzko and H. S. Wilf, The editor's corner: n coins in a fountain, Amer. Math. Monthly, 95 (1988), 840-843.
FORMULA
G.f.: (1-x)/(1-x/(1-x^2/(1-x^3/(1-x^4/(1-x^5/(...)))))).
MAPLE
b:= proc(n, i) option remember; `if`(n=0, 1,
add(b(n-j, j), j=1..min(i+1, n)))
end:
a:= n-> b(n, 0) -b(n-1, 0):
seq(a(n), n=0..50); # Alois P. Heinz, Sep 02 2017
MATHEMATICA
b[n_, i_] := b[n, i] = If[n==0, 1, Sum[b[n-j, j], {j, 1, Min[i+1, n]}]];
a[n_] := b[n, 0] - b[n-1, 0];
a /@ Range[0, 50] (* Jean-François Alcover, Nov 14 2020, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 02 2017
STATUS
approved