%I #27 Mar 07 2024 11:13:57

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

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

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

%N Period 8 zigzag sequence; repeat [0, 1, 2, 3, 4, 3, 2, 1].

%C Decimal expansion of 1111/90009. - _Elmo R. Oliveira_, Mar 03 2024

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,-1,1).

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

%F a(n) = a(n-1) - a(n-4) + a(n-5) for n > 4.

%F a(n) = Sum_{i = 1..n} (-1)^floor((i-1)/4).

%F a(2n) = 2*A007877(n); a(2n+1) = A084101(n).

%F a(n) = abs(n - 8*round(n/8)). - _Jon E. Schoenfield_, Jan 01 2016

%F Euler transform of length 8 sequence [2, 0, 0, -2, 0, 0, 0, 1]. - _Michael Somos_, Feb 27 2020

%F a(n) = a(n-8) for n >= 8. - _Wesley Ivan Hurt_, Sep 07 2022

%e G.f. = x + 2*x^2 + 3*x^3 + 4*x^4 + 3*x^5 + 2*x^6 + x^7 + x^9 + ... - _Michael Somos_, Feb 27 2020

%p A266313:=n->[0, 1, 2, 3, 4, 3, 2, 1][(n mod 8)+1]: seq(A266313(n), n=0..100);

%t CoefficientList[Series[x*(1 + x + x^2 + x^3)/(1 - x + x^4 - x^5), {x, 0, 100}], x]

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

%o (PARI) x='x+O('x^100); concat(0, Vec(x*(1+x+x^2+x^3)/(1-x+x^4-x^5))) \\ _Altug Alkan_, Dec 29 2015

%o (PARI) {a(n) = abs((n+4)\8*8-n)}; /* _Michael Somos_, Feb 27 2020 */

%Y Period k zigzag sequences: A000035 (k=2), A007877 (k=4), A260686 (k=6), this sequence (k=8), A271751 (k=10), A271832 (k=12), A279313 (k=14), A279319 (k=16), A158289 (k=18).

%Y Cf. A084101.

%K nonn,easy

%O 0,3

%A _Wesley Ivan Hurt_, Dec 26 2015