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Search: id:A079998
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| A079998 |
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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=2, r=3, I={-1,0,1,2}. |
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+0
4
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| 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 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=5k, a(n)=0 otherwise. Also, number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=1, r=4, I={0,1,2,3}.
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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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FORMULA
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Recurrence: a(n) = a(n-5) G.f.: -1/(x^5-1)
a(n)={{[4*cos(n*2*Pi/5)+1]^2}/5-1}/4 or a(n)={{8*[sin(n*2*Pi/5)]^2-5}^2-5}/20 - Paolo P. Lava (ppl(AT)spl.at), Aug 24 2006
a(n)=1-(n^4 mod 5) with n>=0 a(n)=1/50*{-9*(n mod 5)+[(n+1) mod 5]+[(n+2) mod 5]+[(n+3) mod 5]+11*[(n+4) mod 5]} with n>=0 - Paolo P. Lava (ppl(AT)spl.at), Nov 29 2006
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CROSSREFS
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Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014.
Adjacent sequences: A079995 A079996 A079997 this_sequence A079999 A080000 A080001
Sequence in context: A014159 A014184 A014359 this_sequence A027356 A097080 A011746
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KEYWORD
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nonn
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AUTHOR
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Vladimir Baltic (baltic(AT)galeb.etf.bg.ac.yu), Feb 10 2003
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