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Period 7: repeat [0, 1, 2, 3, 3, 2, 1].
2

%I #15 Sep 08 2022 08:46:18

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

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

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

%N Period 7: repeat [0, 1, 2, 3, 3, 2, 1].

%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 G.f.: x*(1 + 2*x + 3*x^2 + 3*x^3 + 2*x^4 + x^5)/(1 - x^7).

%F a(n) = (1/2) * Sum_{i=1..2n} (-1)^floor((i-1)/7).

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

%F a(n) = A279313(2n)/2.

%F a(n) = -m*(m^5 - 21*m^4 + 160*m^3 - 525*m^2 + 739*m - 714)/360 where m = n mod 7. - _Luce ETIENNE_, Nov 18 2018

%p a:=n->[0, 1, 2, 3, 3, 2, 1][(n mod 7)+1]: seq(a(n), n=0..300);

%t CoefficientList[Series[x*(1 + 2*x + 3*x^2 + 3*x^3 + 2*x^4 + x^5)/(1 - x^7), {x, 0, 100}], x]

%t PadRight[{}, 120, {0, 1, 2, 3, 3, 2, 1}] (* _Vincenzo Librandi_, Dec 10 2016 *)

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

%Y Cf. A279313.

%Y Cf. A010876.

%K nonn,easy

%O 0,3

%A _Wesley Ivan Hurt_, Dec 09 2016