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A271751
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Period 10 zigzag sequence; repeat: [0, 1, 2, 3, 4, 5, 4, 3, 2, 1].
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10
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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, 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, 2, 1, 0, 1, 2, 3, 4, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5
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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 (1,0,0,0,-1,1).
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FORMULA
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G.f.: x*(1 + x + x^2 + x^3 + x^4)/(1 - x + x^5 - x^6).
a(n) = a(n-1) - a(n-5) + a(n-6) for n>5.
a(n) = abs(n - 10*round(n/10)).
a(n) = Sum_{i=1..n} (-1)^floor((i-1)/5).
a(2n) = 2*abs(A117444(n)).
a(2n+7) = 2*A076839(n)-1 for n>0.
a(n) = a(n-10) for n >= 10. - Wesley Ivan Hurt, Sep 07 2022
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MAPLE
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a:=n->[0, 1, 2, 3, 4, 5, 4, 3, 2, 1][(n mod 10)+1]: seq(a(n), n=0..100);
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MATHEMATICA
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CoefficientList[Series[x*(1 + x + x^2 + x^3 + x^4)/(1 - x + x^5 - x^6), {x, 0, 30}], x]
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PROG
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(Magma) &cat[[0, 1, 2, 3, 4, 5, 4, 3, 2, 1]: n in [0..10]];
(PARI) a(n) = abs(n-10*round(n/10)); \\ Altug Alkan, Apr 13 2016
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CROSSREFS
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Cf. A076839, A117444.
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).
Sequence in context: A237985 A143055 A339388 * A017890 A134011 A280913
Adjacent sequences: A271748 A271749 A271750 * A271752 A271753 A271754
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KEYWORD
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nonn,easy
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AUTHOR
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Wesley Ivan Hurt, Apr 13 2016
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STATUS
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approved
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