A289080 a(0) = 1 and a(n) = A005169(n) - A005169(n-1).

1, 0, 0, 1, 1, 2, 4, 6, 11, 19, 33, 57, 99, 172, 298, 518, 898, 1559, 2706, 4696, 8151, 14147, 24554, 42617, 73969, 128384, 222831, 386759, 671282, 1165118, 2022251, 3509944, 6092077, 10573790, 18352530, 31853801, 55287454, 95960372, 166554844, 289083043

Offset: 0

Author

Seiichi Manyama, Sep 02 2017

Keywords

• nonn

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.

Crossrefs

Column 2 of A288267 (except a(0)).

Cf. A005169.

Programs

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 *)

Formula

G.f.: (1-x)/(1-x/(1-x^2/(1-x^3/(1-x^4/(1-x^5/(...)))))).