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A239002 Number of partitions of n into distinct parts all of which are Fibonacci numbers greater than 1. 8
1, 0, 1, 1, 0, 2, 0, 1, 2, 0, 2, 1, 0, 3, 0, 2, 2, 0, 3, 0, 1, 3, 0, 3, 2, 0, 4, 0, 2, 3, 0, 3, 1, 0, 4, 0, 3, 3, 0, 5, 0, 2, 4, 0, 4, 2, 0, 5, 0, 3, 3, 0, 4, 0, 1, 4, 0, 4, 3, 0, 6, 0, 3, 5, 0, 5, 2, 0, 6, 0, 4, 4, 0, 6, 0, 2, 5, 0, 5, 3, 0, 6, 0, 3, 4, 0, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

a(n) > 0 if n+1 is a term of the lower Wythoff sequence, A000201; a(n) = 0 if n+1 is a term of the upper Wythoff sequence, A001950.

LINKS

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

FORMULA

G.f.: Product_{i>=3} (1+x^Fibonacci(i)). - Alois P. Heinz, Mar 15 2014

MAPLE

F:= combinat[fibonacci]:

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<3, 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, 3, 75}];  b[n_] := SeriesCoefficient[Product[1 + x^f[[k]], {k, n}], {x, 0, n}]; u = Table[b[n], {n, 0, 60}]  (* A239002 *)

Flatten[Position[u, 0]]  (* A001950 *)

CROSSREFS

Cf. A000201, A001950, A000045, A000119, A239003, A000009.

Sequence in context: A035445 A053603 A085794 * A004548 A125921 A321457

Adjacent sequences:  A238999 A239000 A239001 * A239003 A239004 A239005

KEYWORD

nonn,easy,look

AUTHOR

Clark Kimberling, Mar 08 2014

STATUS

approved

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Last modified July 21 06:55 EDT 2019. Contains 325192 sequences. (Running on oeis4.)