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Search: id:A079978
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| A079978 |
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Number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=1, r=2, I={0,1}. |
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+0
10
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| 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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a(n)=1 if n=3k, a(n)=0 otherwise. Decimal expansion of 1/999.
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REFERENCES
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D. H. Lehmer, Permutations with strongly restricted displacements. Combinatorial theory and its applications, II (Proc. Colloq., Balatonfured, 1969), pp. 755-770. North-Holland, Amsterdam, 1970.
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LINKS
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Index entries for characteristic functions
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FORMULA
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Recurrence: a(n) = a(n-3). G.f.: -1/(x^3-1)
a(n)=(1+e^(i*pi*A002487(n)))/2, i=sqrt(-1); - Paul Barry (pbarry(AT)wit.ie), Jan 14 2005
a(n) = (2/3)*[cos(n*(2/3)* Pi)+1/2] with n>=0. This can be used to create any periodic sequence of three elements x, y, z: b(n) = x*a(n) + y*a(n+2) + z*a(n+1) with n>=0 - Paolo P. Lava (ppl(AT)spl.at), Aug 22 2006
Additive with a(p^e) = 1 if p = 3, 0 otherwise.
a(n)=-1*((n^2 mod 3)-1) - Paolo P. Lava (ppl(AT)spl.at), Oct 02 2006
a(n)=((n+1) mod 3) mod 2. Also: a(n)=1/2*(1+(-1)^(n+floor((n+1)/3))). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), May 29 2007
a(n) = 1 - A011655(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 30 2009]
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PROGRAM
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(PARI) a(n)=!(n%3) [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Mar 01 2009]
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CROSSREFS
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Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014, A022003.
Essentially the same as A022003.
Partial sums are given by A002264(n+3).
Sequence in context: A014099 A037011 A024692 this_sequence A164704 A068429 A011747
Adjacent sequences: A079975 A079976 A079977 this_sequence A079979 A079980 A079981
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KEYWORD
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nonn,new
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AUTHOR
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Vladimir Baltic (baltic(AT)matf.bg.ac.yu), Feb 17 2003
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