OFFSET
0,4
COMMENTS
Number of 0's in Zeckendorf-binary representation of n. For example, the Zeckendorf representation of 12 is 8+3+1, which is 10101 in binary notation.
For n > 0: number of zeros in n-th row of A213676, or, number of zeros in n-th row of A189920. - Reinhard Zumkeller, Mar 10 2013
REFERENCES
E. Zeckendorf, Représentation des nombres naturels par une somme des nombres de Fibonacci ou de nombres de Lucas, Bull. Soc. Roy. Sci. Liège 41, 179-182, 1972.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..10946
Ron Knott, General Fibonacci Series
MAPLE
F:= combinat[fibonacci]:
b:= proc(n) option remember; local j;
if n=0 then 0
else for j from 2 while F(j+1)<=n do od;
b(n-F(j))+2^(j-2)
fi
end:
a:= proc(n) local c, m;
c, m:= 0, b(n);
while m>0 do c:= c +1 -irem(m, 2, 'm');
od; c
end:
seq(a(n), n=0..150); # Alois P. Heinz, May 18 2012
MATHEMATICA
F = Fibonacci; b[n_] := b[n] = Module[{j}, If[n==0, 0, For[j=2, F[j+1] <= n, j++]; b[n-F[j]]+2^(j-2)]]; a[n_] := Module[{c, m}, {c, m} = {0, b[n]}; While[m>0, c = c + 1 - Mod[m, 2]; m = Floor[m/2]]; c]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Jan 09 2016, after Alois P. Heinz *)
PROG
(Haskell)
a102364 0 = 0
a102364 n = length $ filter (== 0) $ a213676_row n
-- Reinhard Zumkeller, Mar 10 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Casey Mongoven, Feb 22 2005
STATUS
approved