|
%I #15 Mar 15 2024 02:22:45
%S 1,7,4,4,7,1,1,7,4,4,7,1,1,7,4,4,7,1,1,7,4,4,7,1,1,7,4,4,7,1,1,7,4,4,
%T 7,1,1,7,4,4,7,1,1,7,4,4,7,1,1,7,4,4,7,1,1,7,4,4,7,1,1,7,4,4,7,1,1,7,
%U 4,4,7,1,1,7,4,4,7,1,1,7,4,4,7,1,1,7,4,4,7,1,1,7,4,4,7,1,1,7,4,4,7,1,1,7,4
%N Period 6: repeat [1, 7, 4, 4, 7, 1].
%C Also: the decimal expansion of 5287/30303. [_R. J. Mathar_, Jan 03 2009]
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,-1,1,-1,1).
%F G.f.: (x^4+6*x^3-2*x^2+6*x+1)/((1-x)*(x^2-x+1)*(1+x+x^2)). a(n) = 4 + 3*A099837(n+2)/2 + 3*A010892(n+4)/2. [_R. J. Mathar_, Jan 03 2009]
%F From _Wesley Ivan Hurt_, Jun 23 2016: (Start)
%F a(n) = a(n-1) - a(n-2) + a(n-3) - a(n-4) + a(n-5) for n>4.
%F a(n) = (8 - 3*cos(n*Pi/3) - 3*cos(2*n*Pi/3) + sqrt(3)*sin(n*Pi/3) + 3*sqrt(3)*sin(2*n*Pi/3))/2. (End)
%p A153349:=n->[1, 7, 4, 4, 7, 1][(n mod 6)+1]: seq(A153349(n), n=0..100); # _Wesley Ivan Hurt_, Jun 23 2016
%t PadRight[{}, 100, {1, 7, 4, 4, 7, 1}] (* _Wesley Ivan Hurt_, Jun 23 2016 *)
%o (Magma) &cat [[1, 7, 4, 4, 7, 1]^^20]; // _Wesley Ivan Hurt_, Jun 23 2016
%Y Cf. A010892, A099837.
%K nonn,easy
%O 0,2
%A _Paul Curtz_, Dec 24 2008
%E Extended by _R. J. Mathar_, Jan 03 2009
|
