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 A143299 Number of terms in the Zeckendorf representation of every number in row n of the Wythoff array. 1
 1, 2, 2, 2, 3, 2, 3, 3, 2, 3, 3, 3, 4, 2, 3, 3, 3, 4, 3, 4, 4, 2, 3, 3, 3, 4, 3, 4, 4, 3, 4, 4, 4, 5, 2, 3, 3, 3, 4, 3, 4, 4, 3, 4, 4, 4, 5, 3, 4, 4, 4, 5, 4, 5, 5, 2, 3, 3, 3, 4, 3, 4, 4, 3, 4, 4, 4, 5, 3, 4, 4, 4, 5, 4, 5, 5, 3, 4, 4, 4, 5, 4, 5, 5, 4, 5, 5, 5, 6, 2, 3, 3, 3, 4, 3, 4, 4, 3, 4, 4, 4, 5, 3, 4, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Every number in a row of the Wythoff array has the same number of Zeckendorf summands as the first number in the row; hence A035513(n) is the number of Zeckendorf summands of A003622(n)=n-1+Floor(n*tau), where tau=(1+sqrt(5))/2. Let M(1) = 1, M(2) = 2 and for n >= 3, M(n) = M(n-1).f(M(n-2)) where f() increments by one and the dot stands for concatenation, then this sequence is 0.M(1).M(2).M(3).M(4)... , see the example. - Joerg Arndt, May 14 2011 LINKS EXAMPLE Row 5 of the Wythoff array is (12, 20, 32, ...) and corresponding Zeckendorf representations all have 3 terms: 12 = 1 + 3 + 8, 20 = 2 + 5 + 13, 32 = 3 + 8 + 21, etc. From Joerg Arndt, May 14 2011: (Start) The sequence as an irregular triangle: 1,        = M(1) 1,        = M(2) 1, 2,     = M(3) = M(2).f(M(1)) 1, 2, 2,  = M(4) = M(3).f(M(2)) 1, 2, 2, 2, 3, 1, 2, 2, 2, 3, 2, 3, 3, 1, 2, 2, 2, 3, 2, 3, 3, 2, 3, 3, 3, 4, 1, 2, 2, 2, 3, 2, 3, 3, 2, 3, 3, 3, 4, 2, 3, 3, 3, 4, 3, 4, 4, 1, 2, 2, 2, 3, 2, 3, 3, 2, 3, 3, 3, 4, 2, 3, 3, 3, 4, 3, 4, 4, 2, 3, 3, 3, ... (End) CROSSREFS Cf. A003622, A035513, A134561. Sequence in context: A281856 A106696 A131839 * A239428 A257497 A266225 Adjacent sequences:  A143296 A143297 A143298 * A143300 A143301 A143302 KEYWORD nonn AUTHOR Clark Kimberling, Aug 05 2008 STATUS approved

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Last modified January 19 17:26 EST 2022. Contains 350466 sequences. (Running on oeis4.)