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A079979
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Characteristic function of multiples of six.
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11
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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, 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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Period 6: repeat [1, 0, 0, 0, 0, 0].
a(n)=1 if n=6k, a(n)=0 otherwise.
Decimal expansion of 1/999999.
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}.
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}.
a(n) is also the number of partitions of n such that each part is six (a(0)=1 because the empty partition has no parts to test equality with six). Hence a(n) is also the number of 2-regular graphs on n vertices with each part having girth exactly six. - Jason Kimberley, Oct 10 2011
This sequence is the Euler transformation of A185016. - Jason Kimberley, Oct 10 2011
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REFERENCES
| 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
| Index to sequences with linear recurrences with constant coefficients, signature (0,0,0,0,0,1).
Index entries for characteristic functions
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FORMULA
| 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 (paoloplava(AT)gmail.com), 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 (paoloplava(AT)gmail.com), Aug 23 2006
a(n) = floor(1/2*cos(n*Pi/3)+1/2) [From Gary Detlefs, (gdetlefs(AT)aol.com), May 16 2011]
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PROG
| (MAGMA) &cat[[1, 0^^5]^^30];
(MAGMA) A079979 := func<n|IsDivisibleBy(n, 6)select 1 else 0>;
[A079979:n in [0..59]]; // Jason Kimberley, Oct 10 2011
(PARI) a(n)=!(n%6) \\ Charles R Greathouse IV, Oct 10 2011
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CROSSREFS
| Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014, A097325.
Characteristic function of multiples of g: A000007 (g=0), A000012 (g=1), A059841 (g=2), A079978 (g=3), A121262 (g=4), A079998 (g=5), this sequence (g=6), A082784 (g=7). - Jason Kimberley, Oct 10 2011
Sequence in context: A016347 A015989 A014189 * A089010 A162289 A122276
Adjacent sequences: A079976 A079977 A079978 * A079980 A079981 A079982
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KEYWORD
| nonn,easy
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AUTHOR
| Vladimir Baltic (baltic(AT)matf.bg.ac.yu), Feb 17 2003
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