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A079979
Characteristic function of multiples of six.
23
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, 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
OFFSET
0,1
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
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.
LINKS
Vladimir Baltic, On the number of certain types of strongly restricted permutations, Applicable Analysis and Discrete Mathematics Vol. 4, No 1 (April, 2010), 119-135
FORMULA
a(n) = a(n-6).
G.f.: 1/(1-x^6).
a(n) = floor((1/2)*cos(n*Pi/3) + 1/2). - Gary Detlefs, May 16 2011
a(n) = floor(n/6) - floor((n-1)/6). - Tani Akinari, Oct 23 2012
a(n) = (((((v^n - w^n)^2)*(2 - (-1)^n)*(w^(2*n) + w^n - 3))^2 - 144)^2)/20736, where w = (-1+i*sqrt(3))/2, v = (1+i*sqrt(3))/2. - Bogart B. Strauss, Sep 20 2013
E.g.f.: (2*cos(sqrt(3)*x/2)*cosh(x/2) + cosh(x))/3. - Vaclav Kotesovec, Feb 15 2015
MATHEMATICA
PadRight[{}, 120, {1, 0, 0, 0, 0, 0}] (* Harvey P. Dale, Feb 19 2013 *)
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
(Scheme) (define (A079979 n) (if (zero? (modulo n 6)) 1 0)) ;; Antti Karttunen, Dec 22 2017
CROSSREFS
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).
Sequence in context: A267417 A014189 A319691 * A288711 A347312 A089010
KEYWORD
nonn,easy
AUTHOR
Vladimir Baltic, Feb 17 2003
EXTENSIONS
More terms from Antti Karttunen, Dec 22 2017
STATUS
approved