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A239003 Number of partitions of n into distinct Fibonacci numbers that are all greater than 2. 2
1, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 1, 0, 2, 0, 0, 2, 0, 1, 0, 0, 3, 0, 0, 2, 0, 2, 0, 0, 3, 0, 0, 1, 0, 3, 0, 0, 3, 0, 2, 0, 0, 4, 0, 0, 2, 0, 3, 0, 0, 3, 0, 1, 0, 0, 4, 0, 0, 3, 0, 3, 0, 0, 5, 0, 0, 2, 0, 4, 0, 0, 4, 0, 2, 0, 0, 5, 0, 0, 3, 0, 3, 0, 0, 4, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,9

COMMENTS

a(n) > 0 if n+1 is a term of A003622; a(n) = 0 if n+1 is a term of A022342.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10946

FORMULA

G.f.: product(1 + x^F(j), j=4..infinity). - Wolfdieter Lang, Mar 15 2014

EXAMPLE

There is one partition for n=0, the empty partition.  All parts are distinct, which means that there are no two parts that are equal. So a(0)=1.

MAPLE

F:= combinat[fibonacci]:

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<4, 0,

       b(n, i-1)+`if`(F(i)>n, 0, b(n-F(i), i-1))))

    end:

a:= proc(n) local j; for j from ilog[(1+sqrt(5))/2](n+1)

       while F(j+1)<=n do od; b(n, j)

    end:

seq(a(n), n=0..100);  # Alois P. Heinz, Mar 15 2014

MATHEMATICA

f = Table[Fibonacci[n], {n, 4, 75}];  b[n_] := SeriesCoefficient[Product[1 + x^f[[k]], {k, n}], {x, 0, n}]; u = Table[b[n], {n, 0, 60}]  (* A239003 *)

Flatten[Position[u, 0]]  (* A022342 *)

CROSSREFS

Cf. A000201, A001950, A000045, A000119, A239002, A000009.

Sequence in context: A084888 A091400 A129448 * A123759 A072453 A307303

Adjacent sequences:  A239000 A239001 A239002 * A239004 A239005 A239006

KEYWORD

nonn,easy,look

AUTHOR

Clark Kimberling, Mar 08 2014

STATUS

approved

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Last modified July 15 16:29 EDT 2019. Contains 325049 sequences. (Running on oeis4.)