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%I #17 Mar 06 2024 04:27:27
%S 0,1,2,3,4,5,6,7,6,5,4,3,2,1,0,1,2,3,4,5,6,7,6,5,4,3,2,1,0,1,2,3,4,5,
%T 6,7,6,5,4,3,2,1,0,1,2,3,4,5,6,7,6,5,4,3,2,1,0,1,2,3,4,5,6,7,6,5,4,3,
%U 2,1,0,1,2,3,4,5,6,7,6,5,4,3,2,1,0,1
%N Period 14 zigzag sequence: repeat [0,1,2,3,4,5,6,7,6,5,4,3,2,1].
%C Decimal expansion of 1111111/90000009. - _Elmo R. Oliveira_, Feb 21 2024
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,-1,1).
%F G.f.: x*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)/(1 - x + x^7 - x^8).
%F a(n) = a(n-1) - a(n-7) + a(n-8) for n > 7.
%F a(n) = abs(n - 14*round(n/14)).
%F a(n) = Sum_{i=1..n} (-1)^floor((i-1)/7).
%F a(2n) = 2*A279316(n), a(2n+1) = A279321(n).
%F a(n) = a(n-14) for n >= 14. - _Wesley Ivan Hurt_, Sep 07 2022
%p A279313:=n->[0, 1, 2, 3, 4, 5, 6, 7, 6, 5, 4, 3, 2, 1][(n mod 14)+1]: seq(A279313(n), n=0..200);
%t CoefficientList[Series[x*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)/(1 - x + x^7 - x^8), {x, 0, 100}], x]
%o (Magma) &cat[[0, 1, 2, 3, 4, 5, 6, 7, 6, 5, 4, 3, 2, 1]: n in [0..10]];
%o (PARI) a(n)=([0,1,0,0,0,0,0,0; 0,0,1,0,0,0,0,0; 0,0,0,1,0,0,0,0; 0,0,0,0,1,0,0,0; 0,0,0,0,0,1,0,0; 0,0,0,0,0,0,1,0; 0,0,0,0,0,0,0,1; 1,-1,0,0,0,0,0,1]^n*[0;1;2;3;4;5;6;7])[1,1] \\ _Charles R Greathouse IV_, Dec 12 2016
%Y Period k zigzag sequences: A000035 (k=2), A007877 (k=4), A260686 (k=6), A266313 (k=8), A271751 (k=10), A271832 (k=12), this sequence (k=14), A279319 (k=16), A158289 (k=18).
%Y Cf. A279316, A279321.
%K nonn,easy
%O 0,3
%A _Wesley Ivan Hurt_, Dec 09 2016
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