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 A166486 Periodic sequence [0,1,1,1] of length 4. 27
 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Sum_{k>0} a(k)/k/3^k = log(5)/4. From Reinhard Zumkeller, Nov 30 2009: (Start) a(n) = 1-A121262(n); characteristic function of numbers that are not multiples of 4; a(A042968(n))=1; a(A008586(n))=0; A033436(n) = Sum{k=0..n} a(k)*(n-k). (End) A190621(n) = n * a(n). LINKS Antti Karttunen, Table of n, a(n) for n = 0..65537 Michael Somos, Rational Function Multiplicative Coefficients Index entries for linear recurrences with constant coefficients, signature (0,0,0,1). FORMULA G.f.: (x + x^2 + x^3) / (1 - x^4) = x * (1 + x + x^2) / ((1 - x) * (1 + x) * (1 + x^2)) = x * (1 - x^3) / ((1 - x) * (1 - x^4)). a(n) = (3 - i^n - (-i)^n - (-1)^n) / 4, where i=sqrt(-1). Multiplicative with a(p^e) = (if p=2 then 0^(e-1) else 1), p prime and e>0. - Reinhard Zumkeller, Nov 30 2009 a(n) = 1/2*((n^3+n) mod 4). - Gary Detlefs, Mar 20 2010 a(n) = (3*(n mod 4)+(n+1 mod 4)+(n+2 mod 4)-(n+3 mod 4))/8 (cf. forms of modular arithmetic of Paolo P. Lava, i.e., see A146094). - Bruno Berselli, Sep 27 2010 a(n) = (Fibonacci(n)*Fibonacci(3n) mod 3)/2. - Gary Detlefs Dec 21 2010 Euler transform of length 4 sequence [ 1, 0, -1, 1]. - Michael Somos, Feb 12 2011 Dirichlet g.f. (1-1/4^s)*zeta(s). - R. J. Mathar, Feb 19 2011 a(n) = Fibonacci(n)^2 mod 3. - Gary Detlefs, May 16 2011 a(n) = -1/4*cos(Pi*n)-1/2*cos(1/2*Pi*n)+3/4. - Leonid Bedratyuk, May 13, 2012 For the general case: the characteristic function of numbers that are not multiples of m is a(n)=floor((n-1)/m)-floor(n/m)+1, m,n > 0. - Boris Putievskiy, May 08 2013 a(n) = ceiling(n/4) - floor(n/4). - Wesley Ivan Hurt, Jun 20 2014 a(n) = a(-n) for all n in Z. - Michael Somos, May 05 2015 For n >= 1, a(n) = A053866(A225546(n)) = A000035(A331733(n)). - Antti Karttunen, Jul 07 2020 a(n) = signum(n mod 4). - Alois P. Heinz, May 12 2021 EXAMPLE G.f. = x + x^2 + x^3 + x^5 + x^6 + x^7 + x^9 + x^10 + x^11 + x^13 + x^14 + ... MAPLE seq(1/2*((n^3+n) mod 4), n=0..50); # Gary Detlefs, Mar 20 2010 MATHEMATICA PadRight[{}, 120, {0, 1, 1, 1}] (* Harvey P. Dale, Jul 04 2013 *) Table[Ceiling[n/4] - Floor[n/4], {n, 0, 100}] (* Wesley Ivan Hurt, Jun 20 2014 *) a[ n_] := Sign[ Mod[n, 4]]; (* Michael Somos, May 05 2015 *) PROG (PARI) {a(n) = !!(n%4)}; (Magma) [Ceiling(n/4)-Floor(n/4) : n in [0..50]]; // Wesley Ivan Hurt, Jun 20 2014 CROSSREFS Cf. A016628, A152822, A164985, A165132. First difference of A057353. Cf. A168185, A145568, A168184, A168182, A168181, A109720, A097325, A011558, A011655, A000035, A010873, A121262. Sequence in context: A284939 A188260 A341625 * A046978 A075553 A131729 Adjacent sequences: A166483 A166484 A166485 * A166487 A166488 A166489 KEYWORD nonn,mult,easy AUTHOR Jaume Oliver Lafont, Oct 15 2009 STATUS approved

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Last modified December 6 08:36 EST 2022. Contains 358605 sequences. (Running on oeis4.)