%I #39 Mar 17 2024 20:54:19

%S 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,

%T 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,

%U 4,3,2,1,0,1,2,3,4,5,6,7,8,9,8,7,6,5

%N Period 18 zigzag sequence: repeat [0,1,2,3,4,5,6,7,8,9,8,7,6,5,4,3,2,1].

%C A toothed or zigzag sequence.

%C Sequence contains only numbers 0..9; abs(a(n+1)-a(n)) = 1.

%C Decimal expansion of 12345679/1000000001. - _Elmo R. Oliveira_, Feb 20 2024

%H Arkadiusz Wesolowski, <a href="/A158289/b158289.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,-1,1).

%F a(18*k+j) = a(18*(k+1)-j) = j for k >= 0, j = 0..9.

%F 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

%F a(n) = Sum_{i=0..n-1} (-1)^floor(i/9). - _Wesley Ivan Hurt_, Jul 25 2015

%F a(n) = abs(n - 18*round(n/18)). - _Wesley Ivan Hurt_, Dec 10 2016

%F a(n) = a(n-18) for n >= 18. - _Wesley Ivan Hurt_, Sep 07 2022

%t a[n_] := If[m = Mod[n, 18]; m <= 9, m, 18-m]; Table[a[n], {n, 0, 85}] (* _Jean-François Alcover_, Jul 19 2013 *)

%t 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 *)

%o (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

%o (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

%o (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

%o (PARI) a(n)=abs(n-round(n/18)*18) \\ _M. F. Hasler_, Jul 27 2015

%Y Cf. A068073 (repeat 1,2,3,2), A028356 (repeat 1,2,3,4,3,2), A130784 (repeat 1,3,2).

%Y 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).

%K easy,nonn

%O 0,3

%A _Jaroslav Krizek_, Mar 15 2009

%E Edited and extended by _Klaus Brockhaus_, Sep 07 2009