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%I #25 Dec 12 2023 07:41:49
%S 1,1,1,1,2,1,1,1,1,2,1,1,1,1,2,1,1,1,1,2,1,1,1,1,2,1,1,1,1,2,1,1,1,1,
%T 2,1,1,1,1,2,1,1,1,1,2,1,1,1,1,2,1,1,1,1,2,1,1,1,1,2,1,1,1,1,2,1,1,1,
%U 1,2,1,1,1,1,2,1,1,1,1,2,1,1,1,1,2,1,1,1,1,2,1,1,1,1,2,1,1,1,1,2,1,1,1,1,2
%N Period 5: repeat [1, 1, 1, 1, 2].
%C Continued fraction expansion of (5+sqrt(65))/8.
%C Decimal expansion of 3704/33333.
%C a(n) = A130782(n+3).
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,1).
%F a(n) = a(n-5) for n > 4; a(0) = 1, a(1) = 1, a(2) = 1, a(3) = 1, a(4) = 2.
%F G.f.: (1+x+x^2+x^3+2*x^4)/(1-x^5).
%F a(n+4) = A198517(n+2) + A198517(n+1) + A198517(n). - _Bruno Berselli_, Nov 02 2011
%F a(n) = floor((n+1)*6/5) - floor((n)*6/5). - _Hailey R. Olafson_, Jul 23 2014
%F a(n) = (2/5)*(3 + cos(4*(n-4)*Pi/5) + cos(2*(n+1)*Pi/5)). - _Wesley Ivan Hurt_, Oct 05 2018
%p A177706:=n->floor(6*(n+1)/5)-floor(6*n/5): seq(A177706(n), n=0..100); # _Wesley Ivan Hurt_, Jul 24 2014
%t Table[Floor[6 (n + 1)/5] - Floor[6 n/5], {n, 0, 100}] (* _Wesley Ivan Hurt_, Jul 24 2014 *)
%o (Magma) &cat[ [1, 1, 1, 1, 2]: k in [1..21] ];
%Y Cf. A130782 (repeat 1, 1, 2, 1, 1), A177707 (decimal expansion of (5+sqrt(65))/8).
%K nonn,cofr,easy
%O 0,5
%A _Klaus Brockhaus_, May 11 2010
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