OFFSET
1,1
COMMENTS
LINKS
T. D. Noe, Table of rows 1 to 49, flattened
FORMULA
Numbers with equal counts of 1's and 0's in their Zeckendorf representation.
From Kevin Ryde, Jul 24 2021: (Start)
T(n,k) = Fibonacci(2*n+2) - Fibonacci(2*(n-k)) - 1.
G.f.: x*y*(2 - 2*x + x^2 - (1 + x + x^2)*x*y + x^3*y^2) / ( (1-x) * (1 - 3*x + x^2) * (1 - x*y) * (1 - 3*x*y + (x*y)^2) ).
(End)
EXAMPLE
Representation of 20 is 101010, three 1's and three 0's, so 20 is in the sequence.
Representation of 22 is 1000001, two 1's and five 0's, so 22 is not in the sequence.
MATHEMATICA
nn = 10; f = Join[{0}, Accumulate[Fibonacci[Range[2, 2*nn, 2] - 1]]]; t = Table[hi = f[[n+1]] - 1; Reverse[Table[hi - f[[i]], {i, n - 1}]], {n, 2, nn}]; t = Flatten[t] (* T. D. Noe, May 08 2012 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Alex Ratushnyak, May 07 2012
STATUS
approved