A238469 - OEIS

%I #21 Dec 12 2023 07:46:43

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

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

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

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

%C This sequence is called B(n) in a comment on A234044 where it appears, together with five others, in a formula for 2*exp(2*Pi*n*I/7). See A234044 for details, also for the n = 4 example.

%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*(1 - x^5)/(1 - x^7).

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

%F From _Wesley Ivan Hurt_, Jul 18 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(n/7) - floor((1+n)/7) - floor((5+n)/7) + floor((6+n)/7). (End)

%p seq(op([0, 1, 0, 0, 0, 0, -1]), n=0..20); # _Wesley Ivan Hurt_, Jul 18 2016

%t PadRight[{}, 100, {0, 1, 0, 0, 0, 0, -1}] (* _Wesley Ivan Hurt_, Jul 18 2016 *)

%o (PARI) a(n)=(n+1)^6%7 - (n+6)^6%7 \\ _Charles R Greathouse IV_, Jul 17 2016

%o (Magma) &cat [[0, 1, 0, 0, 0, 0, -1]^^20]; // _Wesley Ivan Hurt_, Jul 18 2016

%Y Cf. A234044, A234045, A234046, A238468, A238470.

%K sign,easy

%O 0

%A _Wolfdieter Lang_, Feb 27 2014