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A035614
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Horizontal para-Fibonacci sequence: says which column of Wythoff array (starting column count at 0) contains n.
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10
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0, 1, 2, 0, 3, 0, 1, 4, 0, 1, 2, 0, 5, 0, 1, 2, 0, 3, 0, 1, 6, 0, 1, 2, 0, 3, 0, 1, 4, 0, 1, 2, 0, 7, 0, 1, 2, 0, 3, 0, 1, 4, 0, 1, 2, 0, 5, 0, 1, 2, 0, 3, 0, 1, 8, 0, 1, 2, 0, 3, 0, 1, 4, 0, 1, 2, 0, 5, 0, 1, 2, 0, 3, 0, 1, 6, 0, 1, 2, 0, 3
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OFFSET
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0,3
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COMMENTS
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This is probably the same as the "Fibonacci ruler function" mentioned by Knuth. - N. J. A. Sloane, Aug 03 2012
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REFERENCES
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D. E. Knuth, The Art of Computer Programming, Vol. 4A, Section 7.1.3, p. 82, solution to Problem 179. - From N. J. A. Sloane, Aug 03 2012
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
N. J. A. Sloane, Classic Sequences
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FORMULA
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The segment between the first M and the first M+1 is given by the segment before the first M-1.
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MATHEMATICA
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max = 81; wy = Table[(n-k)*Fibonacci[k] + Fibonacci[k+1]*Floor[ GoldenRatio*(n - k + 1)], {n, 1, max}, {k, 1, n}]; a[n_] := Position[wy, n][[1, 2]]-1; Table[a[n], {n, 1, max}] (* From Jean-François Alcover, Nov 02 2011 *)
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PROG
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(Haskell)
a035614 = a122840 . a014417 . (+ 1) -- Reinhard Zumkeller, Mar 10 2013
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CROSSREFS
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Cf. A019586, A035513, A035614.
Sequence in context: A160271 A065134 A088673 * A212138 A133735 A095704
Adjacent sequences: A035611 A035612 A035613 * A035615 A035616 A035617
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KEYWORD
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nonn,nice,easy
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AUTHOR
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J. H. Conway, N. J. A. Sloane.
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STATUS
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approved
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