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A158289
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Period 18 zigzag sequence: repeat [0,1,2,3,4,5,6,7,8,9,8,7,6,5,4,3,2,1].
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13
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0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5
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OFFSET
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0,3
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COMMENTS
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A toothed or zigzag sequence.
Sequence contains only numbers 0..9; abs(a(n+1)-a(n)) = 1.
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LINKS
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Arkadiusz Wesolowski, Table of n, a(n) for n = 0..10000
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FORMULA
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a(18*k+j) = a(18*(k+1)-j) = j for k >= 0, j = 0..9.
G.f.: x*(1+x+x^2)*(1+x^3+x^6)/((1-x)*(1+x)*(1-x+x^2)*(1-x^3+x^6)). - Klaus Brockhaus, Sep 07 2009
a(n) = (1/153)*{13*(n mod 18)+13*[(n+1) mod 18]+13*[(n+2) mod 18]+13*[(n+3) mod 18]+13*[(n+4) mod 18]+13*[(n+5) mod 18]+13*[(n+6) mod 18]+13*[(n+7) mod 18]+13*[(n+8) mod 18]-4*[(n+9) mod 18]-4*[(n+10) mod 18]-4*[(n+11) mod 18]-4*[(n+12) mod 18]-4*[(n+13) mod 18]-4*[(n+14) mod 18]-4*[(n+15) mod 18]-4*[(n+16) mod 18]-4*[(n+17) mod 18]}, with n>=0. - Paolo P. Lava, Nov 12 2009
a(n) = Sum_{i=0..n-1} (-1)^floor(i/9). - Wesley Ivan Hurt, Jul 25 2015
a(n) = abs(n - 18*round(n/18)). - Wesley Ivan Hurt, Dec 10 2016
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MATHEMATICA
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a[n_] := If[m = Mod[n, 18]; m <= 9, m, 18-m]; Table[a[n], {n, 0, 85}] (* Jean-François Alcover, Jul 19 2013 *)
PadRight[{}, 100, {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1}] (* Vincenzo Librandi, Jul 26 2015 *)
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PROG
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(MAGMA) [ s lt 9 select r else 9-r where r is n mod 9 where s is n mod 18: n in [0..104] ]; // Klaus Brockhaus, Sep 07 2009
(MAGMA) S:=[]; a:=0; for n in [0..104] do Append(~S, a); if n mod 18 eq 0 then d:=1; else if n mod 9 eq 0 then d:=-1; end if; end if; a+:=d; end for; S; // Klaus Brockhaus, Sep 07 2009
(MAGMA) &cat[[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2, 1]: n in [0..5]]; // Vincenzo Librandi, Jul 26 2015
(PARI) a(n)=abs(n-round(n/18)*18) \\ M. F. Hasler, Jul 27 2015
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CROSSREFS
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Cf. A068073 (repeat 1,2,3,2), A028356 (repeat 1,2,3,4,3,2), A130784 (repeat 1,3,2).
Period k zigzag sequences: A000035 (k=2), A007877 (k=4), A260686 (k=6), A266313 (k=8), A271751 (k=10), A271832 (k=12), A279313 (k=14), A279319 (k=16), this sequence (k=18).
Sequence in context: A028902 A081598 A232360 * A213652 A262734 A287794
Adjacent sequences: A158286 A158287 A158288 * A158290 A158291 A158292
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KEYWORD
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easy,nonn
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AUTHOR
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Jaroslav Krizek, Mar 15 2009
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EXTENSIONS
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Edited and extended by Klaus Brockhaus, Sep 07 2009
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STATUS
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approved
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