A178141 - OEIS

%I #21 Dec 12 2023 07:41:39

%S 4,-1,2,-4,1,2,4,-1,2,-4,1,2,4,-1,2,-4,1,2,4,-1,2,-4,1,2,4,-1,2,-4,1,

%T 2,4,-1,2,-4,1,2,4,-1,2,-4,1,2,4,-1,2,-4,1,2,4,-1,2,-4,1,2,4,-1,2,-4,

%U 1,2,4,-1,2,-4,1,2,4,-1,2,-4,1,2,4,-1,2,-4,1,2

%N Period 6: repeat [4, -1, 2, -4, 1, 2].

%C Differences of the period 6: repeat [1, 5, 4, 6, 2, 3] (A070365).

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,1).

%F Mix A153727(n+1) with -A153727(n).

%F From _Wesley Ivan Hurt_, Jun 23 2016: (Start)

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

%F a(n) = a(n-6) for n>5.

%F a(n) = (2 + 5*cos(n*Pi) + 7*cos(n*Pi/3) - 2*cos(2*n*Pi/3) - sqrt(3)*sin(n*Pi/3) - 2*sqrt(3)*sin(2*n*Pi/3))/3. (End)

%p A178141:=n->[4, -1, 2, -4, 1, 2][(n mod 6)+1]: seq(A178141(n), n=0..100); # _Wesley Ivan Hurt_, Jun 23 2016

%t PadRight[{}, 100, {4, -1, 2, -4, 1, 2}] (* _Wesley Ivan Hurt_, Jun 23 2016 *)

%o (PARI) a(n)=[1,5,4,6,2,3][n%5+1] \\ _Charles R Greathouse IV_, Jun 02 2011

%o (Magma) &cat [[4, -1, 2, -4, 1, 2]^^20]; // _Wesley Ivan Hurt_, Jun 23 2016

%Y Cf. A069705, A070365, A132954, A153727.

%K sign,easy,less

%O 0,1

%A _Paul Curtz_, May 21 2010

%E New name from _Wesley Ivan Hurt_, Jun 23 2016