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Period 7: repeat [1, 3, 5, 7, 5, 3, 1].
2

%I #17 Sep 08 2022 08:46:18

%S 1,3,5,7,5,3,1,1,3,5,7,5,3,1,1,3,5,7,5,3,1,1,3,5,7,5,3,1,1,3,5,7,5,3,

%T 1,1,3,5,7,5,3,1,1,3,5,7,5,3,1,1,3,5,7,5,3,1,1,3,5,7,5,3,1,1,3,5,7,5,

%U 3,1,1,3,5,7,5,3,1,1,3,5,7,5,3,1,1,3

%N Period 7: repeat [1, 3, 5, 7, 5, 3, 1].

%H Colin Barker, <a href="/A279321/b279321.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,1).

%F a(n) = abs(2n + 1 - 14*round((2n + 1)/14)).

%F a(n) = (25 + 2*( ((n+1) mod 7) + ((n+2) mod 7) + ((n+3) mod 7) - ((n+4) mod 7) - ((n+5) mod 7) - ((n+6) mod 7) ))/7. - _Wesley Ivan Hurt_, Dec 23 2016

%F From _Colin Barker_, Mar 21 2019: (Start)

%F G.f.: (1 + 2*x + x^2 + x^3)*(1 + x + 2*x^2 + x^3) / ((1 - x)*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)).

%F a(n) = a(n-7) for n>6.

%F (End)

%p A279321:=n->[1, 3, 5, 7, 5, 3, 1, 1][(n mod 7)+1]: seq(A279321(n), n=0..100); # _Wesley Ivan Hurt_, Dec 23 2016

%t PadRight[{}, 120, {1, 3, 5, 7, 5, 3, 1}] (* _Vincenzo Librandi_, Dec 10 2016 *)

%t With[{k = 14}, Table[Abs[2 n + 1 - k Round[(2 n + 1)/k]], {n, 0, 120}]] (* _Michael De Vlieger_, Dec 10 2016 *)

%o (Magma) &cat[[1, 3, 5, 7, 5, 3, 1]: n in [0..10]];

%o (PARI) Vec((1 + 2*x + x^2 + x^3)*(1 + x + 2*x^2 + x^3) / ((1 - x)*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)) + O(x^85)) \\ _Colin Barker_, Mar 21 2019

%Y Bisection of A279313.

%K nonn,easy

%O 0,2

%A _Wesley Ivan Hurt_, Dec 09 2016