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Search: id:A079979
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| A079979 |
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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=3, r=3, I={-2,-1,0,1,2}. |
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+0
2
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| 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 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=6k, a(n)=0 otherwise. Decimal expansion of 1/999999. Also, number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, i=1..n, with k=1, r=5, I={0,1,2,3,4}.
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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-6) G.f.: -1/(x^6-1)
a(n) = (1/3)*[cos(n*(2/3)* Pi)+1/2]*[1+(-1)^n] with n>=0 - Paolo P. Lava (ppl(AT)spl.at), Aug 23 2006
This formula can be used to produce any periodic sequence of 6 numbers b,c,d,e,f,g: a(n)= b*(1/3)*[cos(n*(2/3)* Pi)+ 1/2]*[1+(-1)^n]+ c*(1/3)*[cos((n+5)*(2/3)* Pi)+ 1/2]*[1+(-1)^(n+5)]+ d*(1/3)*[cos((n+4)*(2/3)* Pi)+ 1/2]*[1+(-1)^(n+4)]+ e*(1/3)*[cos((n+3)*(2/3)* Pi)+ 1/2]*[1+(-1)^(n+3)]+ f*(1/3)*[cos((n+2)*(2/3)* Pi)+ 1/2]*[1+(-1)^(n+2)]+ g*(1/3)*[cos((n+1)*(2/3)* Pi)+ 1/2]*[1+(-1)^(n+1)] - Paolo P. Lava (ppl(AT)spl.at), Aug 23 2006
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CROSSREFS
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Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014.
Cf. A097325.
Sequence in context: A016347 A015989 A014189 this_sequence A089010 A122276 A066288
Adjacent sequences: A079976 A079977 A079978 this_sequence A079980 A079981 A079982
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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 17 2003
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