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 A131719 Period 6: repeat [0, 1, 1, 1, 1, 0]. 5

%I

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

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

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

%N Period 6: repeat [0, 1, 1, 1, 1, 0].

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,-1,1,-1,1).

%F a(n) = (1/90)*{4*(n mod 6)+19*[(n+1) mod 6]+4*[(n+2) mod 6]+4*[(n+3) mod 6]+4*[(n+4) mod 6]-11*[(n+5) mod 6]}. - _Paolo P. Lava_, Oct 02 2007

%F G.f.: -(x^2+1)*x/(x-1)/(x^2+x+1)/(x^2-x+1). - _R. J. Mathar_, Nov 14 2007

%F a(n) = 2/3-cos(Pi*n/3)/2+sqrt(3)*sin(Pi*n/3)/6 -cos(2*Pi*n/3)/6 +sqrt(3)*sin(2*Pi*n/3)/6. - _R. J. Mathar_, Oct 08 2011

%F a(n) = a(n-1) - a(n-2) + a(n-3) - a(n-4) + a(n-5) for n>4. - _Wesley Ivan Hurt_, Jun 19 2016

%F a(n+3) = A000358(n)(mod 2), for n>0. - _John M. Campbell_, Jul 08 2016

%p A131719:=n->[0, 1, 1, 1, 1, 0][(n mod 6)+1]: seq(A131719(n), n=0..100); # _Wesley Ivan Hurt_, Jun 19 2016

%t PadRight[{}, 200, {0, 1, 1, 1, 1, 0}] (* _Wesley Ivan Hurt_, Jun 19 2016 *)

%o (PARI) a(n)=[0,1,1,1,1,0][n%6+1] \\ _Charles R Greathouse IV_, Jun 02 2011

%o (MAGMA) &cat[[0, 1, 1, 1, 1, 0]^^20]; // _Wesley Ivan Hurt_, Jun 19 2016

%K nonn,easy,less

%O 0,1

%A _Paul Curtz_, Sep 15 2007

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Last modified April 8 21:44 EDT 2020. Contains 333329 sequences. (Running on oeis4.)