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%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
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