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 A271751 Period 10 zigzag sequence; repeat: [0, 1, 2, 3, 4, 5, 4, 3, 2, 1]. 8

%I

%S 0,1,2,3,4,5,4,3,2,1,0,1,2,3,4,5,4,3,2,1,0,1,2,3,4,5,4,3,2,1,0,1,2,3,

%T 4,5,4,3,2,1,0,1,2,3,4,5,4,3,2,1,0,1,2,3,4,5,4,3,2,1,0,1,2,3,4,5,4,3,

%U 2,1,0,1,2,3,4,5,4,3,2,1,0,1,2,3,4,5

%N Period 10 zigzag sequence; repeat: [0, 1, 2, 3, 4, 5, 4, 3, 2, 1].

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,-1,1).

%F G.f.: x*(1 + x + x^2 + x^3 + x^4)/(1 - x + x^5 - x^6).

%F a(n) = a(n-1) - a(n-5) + a(n-6) for n>5.

%F a(n) = abs(n - 10*round(n/10)).

%F a(n) = Sum_{i=1..n} (-1)^floor((i-1)/5).

%F a(2n) = 2*abs(A117444(n)).

%F a(2n+7) = 2*A076839(n)-1 for n>0.

%p a:=n->[0, 1, 2, 3, 4, 5, 4, 3, 2, 1][(n mod 10)+1]: seq(a(n), n=0..100);

%t CoefficientList[Series[x*(1 + x + x^2 + x^3 + x^4)/(1 - x + x^5 - x^6), {x, 0, 30}], x]

%o (MAGMA) &cat[[0, 1, 2, 3, 4, 5, 4, 3, 2, 1]: n in [0..10]];

%o (PARI) a(n) = abs(n-10*round(n/10)); \\ _Altug Alkan_, Apr 13 2016

%Y Cf. A076839, A117444.

%Y Period k zigzag sequences: A000035 (k=2), A007877 (k=4), A260686 (k=6), A266313 (k=8), this sequence (k=10), A271832 (k=12), A279313 (k=14), A279319 (k=16), A158289 (k=18).

%K nonn,easy

%O 0,3

%A _Wesley Ivan Hurt_, Apr 13 2016

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Last modified November 16 06:50 EST 2018. Contains 317258 sequences. (Running on oeis4.)