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A260686
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Period 6 zigzag sequence, repeat [0, 1, 2, 3, 2, 1].
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10
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0, 1, 2, 3, 2, 1, 0, 1, 2, 3, 2, 1, 0, 1, 2, 3, 2, 1, 0, 1, 2, 3, 2, 1, 0, 1, 2, 3, 2, 1, 0, 1, 2, 3, 2, 1, 0, 1, 2, 3, 2, 1, 0, 1, 2, 3, 2, 1, 0, 1, 2, 3, 2, 1, 0, 1, 2, 3, 2, 1, 0, 1, 2, 3, 2, 1, 0, 1, 2, 3, 2, 1, 0, 1, 2, 3, 2, 1, 0, 1, 2, 3, 2, 1, 0, 1
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..85.
Index entries for linear recurrences with constant coefficients, signature (1,0,-1,1).
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FORMULA
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G.f.: x*(1 + x + x^2) / (1 - x + x^3 - x^4).
a(n) = a(n-1) - a(n-3) + a(n-4) for n>3.
a(n) = Sum_{i=1..n} (-1)^floor((i-1)/3) for n>0.
a(n+1) = a(n) + A130151(n).
a(2n) = 2*A011655(n), a(2n+1) = A109007(n+2).
a(n) = 1 + (1 - (-1)^n)/2 - (-1)^floor((n+1)/3). [Bruno Berselli, Nov 16 2015]
a(n) = sin(n*Pi/6)^2*(11+4*cos(n*Pi/3)+2*cos(2*n*Pi/3))/3. - Wesley Ivan Hurt, Jun 17 2016
a(n) = 3/2-1/6*(-1)^n-2/3*((1/2-(1/2*I)*sqrt(3))^n+(1/2+(1/2*I)*sqrt(3))^n) where I=sqrt(-1). - Paolo P. Lava, Jun 17 2016
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MAPLE
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A260686:=n->[0, 1, 2, 3, 2, 1][(n mod 6)+1]: seq(A260686(n), n=0..100);
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MATHEMATICA
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CoefficientList[Series[(x + x^2 + x^3)/(1 - x + x^3 - x^4), {x, 0, 100}], x]
Table[1 + (1 - (-1)^n)/2 - (-1)^Floor[(n + 1)/3], {n, 0, 100}] (* Bruno Berselli, Nov 16 2015 *)
PadRight[{}, 120, {0, 1, 2, 3, 2, 1}] (* Vincenzo Librandi, Nov 17 2015 *)
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PROG
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(PARI) concat(0, Vec((x+x^2+x^3)/(1-x+x^3-x^4) + O(x^100))) \\ Altug Alkan, Nov 15 2015
(MAGMA) [1+(1-(-1)^n)/2-(-1)^Floor((n+1)/3): n in [0..100]]; // Bruno Berselli, Nov 16 2015
(MAGMA) &cat[[0, 1, 2, 3, 2, 1]: n in [0..15]]; // Vincenzo Librandi, Nov 17 2015
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CROSSREFS
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Period k zigzag sequences: A000035 (k=2), A007877 (k=4), this sequence (k=6), A266313 (k=8), A271751 (k=10), A271832 (k=12), A279313 (k=14), A279319 (k=16), A158289 (k=18).
Cf. A011655, A109007, A130151.
Sequence in context: A059285 A165578 A020990 * A037891 A037899 A037837
Adjacent sequences: A260683 A260684 A260685 * A260687 A260688 A260689
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KEYWORD
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nonn,easy
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AUTHOR
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Wesley Ivan Hurt, Nov 15 2015
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STATUS
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approved
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