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%I
%S 0,1,2,3,3,1,5,5,1,5,2,8,8,1,8,2,8,3,8,3,1,13,13,1,13,2,13,3,13,3,1,
%T 13,5,13,5,1,13,5,2,21,21,1,21,2,21,3,21,3,1,21,5,21,5,1,21,5,2,21,8,
%U 21,8,1,21,8,2,21,8,3,21,8,3,1,34,34,1,34,2,34,3,34,3,1,34,5,34,5,1,34,5,2
%N Triangular array formed from Zeckendorf expansion of integers: repeatedly subtract the largest Fibonacci number you can until nothing remains.
%C Row n has A007895(n) terms.
%D Zeckendorf, E., Representation des nombres naturels par une somme des nombres de Fibonacci ou de nombres de Lucas, Bull. Soc. Roy. Sci. Liege 41, 179-182, 1972.
%H T. D. Noe, <a href="/A035516/b035516.txt">Rows n=0..1000 of triangle, flattened</a>
%H N. J. A. Sloane, <a href="/classic.html#WYTH">Classic Sequences</a>
%e 16 = 13 + 3.
%e 0; 1; 2; 3; 3,1; 5; 5,1; 5,2; 8; 8,1; 8,2; ...
%o (Haskell)
%o a035516 n k = a035516_tabf !! n !! k
%o a035516_tabf = map a035516_row [0..]
%o a035516_row 0 = [0]
%o a035516_row n = z n $ reverse $ takeWhile (<= n) a000045_list where
%o z 0 _ = []
%o z x (f:fs'@(_:fs)) = if f <= x then f : z (x - f) fs else z x fs'
%o -- _Reinhard Zumkeller_, Mar 10 2013
%Y Cf. A035517, A035514, A035515.
%Y Cf. A000045.
%K nonn,easy,tabf
%O 0,3
%A _N. J. A. Sloane_.
%E More terms from _James A. Sellers_, Dec 13 1999
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