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A289080 a(0) = 1 and a(n) = A005169(n) - A005169(n-1). 2
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

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

CROSSREFS

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

Cf. A005169.

Sequence in context: A116732 A048239 A000786 * A000694 A164137 A018170

Adjacent sequences:  A289077 A289078 A289079 * A289081 A289082 A289083

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Sep 02 2017

STATUS

approved

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Last modified October 22 01:42 EDT 2018. Contains 316431 sequences. (Running on oeis4.)