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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

Table of n, a(n) for n=1..105.

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 October 1 08:39 EDT 2020. Contains 337442 sequences. (Running on oeis4.)