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 A079979 Characteristic function of multiples of six. 20
 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 (list; graph; refs; listen; history; text; internal format)
 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 Antti Karttunen, Table of n, a(n) for n = 0..65538 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 Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1). FORMULA a(n) = a(n-6). G.f.: 1/(1-x^6). a(n) = (1/3)*(cos(n*(2/3)*Pi) + 1/2)*(1+(-1)^n) with n>=0. - Paolo P. Lava, 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, Aug 23 2006 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; [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 Cf. A002524-A002529, A010875, A072827, A072850-A072856, A079955-A080014, A097325, A122841. 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 Adjacent sequences:  A079976 A079977 A079978 * A079980 A079981 A079982 KEYWORD nonn,easy AUTHOR Vladimir Baltic, Feb 17 2003 EXTENSIONS More terms from Antti Karttunen, Dec 22 2017 STATUS approved

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Last modified September 24 21:05 EDT 2021. Contains 347651 sequences. (Running on oeis4.)