A234045 - OEIS

%I #13 Sep 08 2022 08:46:06

%S 0,0,1,-1,-1,1,0,0,0,1,-1,-1,1,0,0,0,1,-1,-1,1,0,0,0,1,-1,-1,1,0,0,0,

%T 1,-1,-1,1,0,0,0,1,-1,-1,1,0,0,0,1,-1,-1,1,0,0,0,1,-1,-1,1,0,0,0,1,-1,

%U -1,1,0,0,0,1,-1,-1,1,0,0,0,1,-1,-1,1,0,0,0,1,-1,-1,1,0,0,0,1,-1,-1,1,0

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

%C This is one of the six sequences appearing in a formula for 2*exp(2*Pi*n*I/7). See A234044 for details. The present sequence there is called b(n). An example for n=4 is also given there.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (-1,-1,-1,-1,-1,-1).

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

%F a(n+7) = a(n), n >= 7, with a(0) = a(1) = a(6) =0 and a(2) = -a(3) = -a(4) = a(5) = 1.

%F From _Wesley Ivan Hurt_, Jul 16 2016: (Start)

%F a(n) + a(n-1) + a(n-2) + a(n-3) + a(n-4) + a(n-5) + a(n-6) = 0, for n>5.

%F a(n) = - floor((1+n)/7) + 2*floor((2+n)/7) - 2*floor((4+n)/7) + floor((5+n)/7). (End)

%p seq(op([0, 0, 1, -1, -1, 1, 0]), n=0..20); # _Wesley Ivan Hurt_, Jul 16 2016

%t PadRight[{}, 100, {0, 0, 1, -1, -1, 1, 0}] (* _Wesley Ivan Hurt_, Jul 16 2016 *)

%o (Magma) &cat [[0, 0, 1, -1, -1, 1, 0]^^20]; // _Wesley Ivan Hurt_, Jul 16 2016

%o (PARI) a(n)=(n+2)\7*2 - (n+1)\7 - (n+4)\7*2 + (n+5)\7 \\ _Charles R Greathouse IV_, Jul 16 2016

%Y Cf. A234044, A234046, A238468, A238469, A238470.

%K sign,easy

%O 0

%A _Wolfdieter Lang_, Feb 27 2014