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Reversed Zeckendorf binary representation of natural numbers.
9

%I #10 Mar 10 2013 16:39:27

%S 0,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0,1,0,0,0,0,1,1,0,0,0,1,0,1,

%T 0,0,1,0,0,1,0,1,1,0,1,0,1,0,0,0,0,0,1,1,0,0,0,0,1,0,1,0,0,0,1,0,0,1,

%U 0,0,1,1,0,1,0,0,1,0,0,0,1,0,1,1,0,0

%N Reversed Zeckendorf binary representation of natural numbers.

%C T(n,k) = A189920(n, A072649(n, k)-1) for k = 0..A072649(k)-1, n > 0;

%C A000201 = row numbers starting with an even number of zeros;

%C for n > 0: A035614(n-1) = number of leading zeros of n-th row.

%H Reinhard Zumkeller, <a href="/A213676/b213676.txt">Rows n = 0..1000 of triangle, flattened</a>

%e The first rows:

%e . 0: [0]

%e . 1: [1]

%e . 2: [0,1]

%e . 3: [0,0,1]

%e . 4: [1,0,1]

%e . 5: [0,0,0,1]

%e . 6: [1,0,0,1]

%e . 7: [0,1,0,1]

%e . 8: [0,0,0,0,1]

%e . 9: [1,0,0,0,1]

%e . 10: [0,1,0,0,1]

%e . 11: [0,0,1,0,1]

%e . 12: [1,0,1,0,1].

%o (Haskell)

%o a213676 n k = a213676_tabf !! n !! k

%o a213676_row n = a213676_tabf !! n

%o a213676_tabf = [0] : map reverse a189920_tabf

%Y Cf. A072649 (row lengths, n>0), A007895 (row sums).

%K nonn,tabf

%O 0

%A _Reinhard Zumkeller_, Mar 10 2013