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Search: id:A007895
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| A007895 |
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Number of terms in Zeckendorf representation of n (write n as a sum of non-consecutive distinct Fibonacci numbers). |
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28
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| 0, 1, 1, 1, 2, 1, 2, 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, 4, 3, 4, 4, 3, 4, 4, 4, 5, 1
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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Let M(0)=0, M(1)=1, and for i > 0, M(i+1)=f(concatenation of M(j), j from 0 to i-1) where f is the morphism f(k)=k+1. Then sequence = concatenation of M(j) for j from 0 to infinity. - Claude Lenormand (claude.lenormand(AT)free.fr), Dec 16 2003
a(n) = A000120(A003714(n)). - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), May 05 2005
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REFERENCES
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D. E. Daykin, Representation of natural numbers as sums of generalized Fibonacci numbers, J. London Math. Soc. 35 (1960) 143-160.
C. G. Lekkerkerker, Voorstelling van natuurlijke getallen door een som van getallen van Fibonacci, Simon Stevin 29 (1952) 190-195.
F. Weinstein, The Fibonacci Partitions, preprint, 1995.
E. Zeckendorf, 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.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..10000
Joerg Arndt, Fxtbook
I. Nemes, Fibonacci representations of multiples of Fibonacci numbers
F. V. Weinstein, Notes on Fibonacci partitions
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FORMULA
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a(n) = A107015(n) + A107016(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), May 09 2005
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EXAMPLE
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a(46) = a(1+3+8+34) = 4.
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CROSSREFS
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Cf. Cf. A035514, A035515, A035516, A035517.
Record positions are in A027941.
Adjacent sequences: A007892 A007893 A007894 this_sequence A007896 A007897 A007898
Sequence in context: A085761 A102382 A024890 this_sequence A136655 A053260 A014643
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KEYWORD
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nonn
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AUTHOR
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Felix Weinstein (wain(AT)ana.unibe.ch), Clark Kimberling (ck6(AT)evansville.edu)
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