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A239002
Number of partitions of n into distinct parts all of which are Fibonacci numbers greater than 1.
9
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
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
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
KEYWORD
nonn,easy,look
AUTHOR
Clark Kimberling, Mar 08 2014
STATUS
approved