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A014677
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First differences of A001468.
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0
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1, -1, 1, 0, -1, 1, -1, 1, 0, -1, 1, 0, -1, 1, -1, 1, 0, -1, 1, -1, 1, 0, -1, 1, 0, -1, 1, -1, 1, 0, -1, 1, 0, -1, 1, -1, 1, 0, -1, 1, -1, 1, 0, -1, 1, 0, -1, 1, -1, 1, 0, -1, 1, -1, 1, 0, -1, 1, 0, -1, 1, -1, 1, 0, -1, 1, 0, -1, 1, -1, 1, 0, -1, 1, -1, 1, 0, -1, 1, 0, -1, 1, -1, 1, 0, -1, 1, 0, -1, 1, -1, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| A001468 is an infinite Fibonacci word with strings of 2's of length A001468(n) delimited by 1's. - Paul D. Hanna (pauldhanna(AT)juno.com), Dec 17 2004
c(n):=a(n-1), n>=1, is -1 if n is a Wythoff B-number from A001950, it is 0 if n=A(B(m)+1) for some m>=1, with A(k):=A000201(k) (Wythoff A-numbers) and it is +1 if n=A(A(m)+1)=B(m)+1 for some m>=0, with B(0):=0. W. Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Oct 13 2006
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FORMULA
| abs(a(n))=floor(f*ceil(n/f))-ceil(f*floor(n/f)) where f=phi=(1+sqrt(5))/2; for n>1 abs(a(n))=A005713(n-1) - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 21 2003
G.f. equals the continued fraction: A(x) = [0;1, 1/x, 1/x, 1/x^2, 1/x^3, 1/x^5, 1/x^8, ..., 1/x^Fibonacci(n), ...]. - Paul D. Hanna (pauldhanna(AT)juno.com), Dec 17 2004
a(n)=b(n)-b(n-1) with b(n):=A005614(n), n>=1.
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CROSSREFS
| Cf. A001468, A000045.
Sequence in context: A076213 A120525 A112299 * A175087 A127872 A129564
Adjacent sequences: A014674 A014675 A014676 * A014678 A014679 A014680
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KEYWORD
| sign
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Nov 07 2001
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