login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A289080 a(0) = 1 and a(n) = A005169(n) - A005169(n-1). 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,6
LINKS
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
Column 2 of A288267 (except a(0)).
Cf. A005169.
Sequence in context: A367736 A048239 A000786 * A000694 A164137 A018170
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Sep 02 2017
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 10:59 EDT 2024. Contains 371277 sequences. (Running on oeis4.)