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%I #85 Apr 20 2024 14:06:03
%S 4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,
%T 4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,4,5,
%U 4,5,4,5,4,5,4,5,4,5,4,5,4
%N Period 2: repeat [4,5].
%C Continued fraction of 2 + 2*sqrt(30)/5 = A176215. - _R. J. Mathar_, Nov 21 2011
%C Decimal expansion of 5/11. - _Franklin T. Adams-Watters_, Jan 25 2019
%C Also, a(n) is the number of binary sequences of length n+3 avoiding the subsequences 000, 001, 011, 111. For example, when n=5 the a(5)=5 sequences of length 8 are 01010101, 10101010, 01010100, 11010101, 11010100. - _Miquel A. Fiol_, Dec 28 2023
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,1).
%F G.f.: (4+5*x)/(1-x^2). - _Jaume Oliver Lafont_, Mar 20 2009
%F a(n) = floor(9*(n+1)/2) - floor(9*n/2). - _Hailey R. Olafson_, Jul 17 2014
%F a(n) = 4 + (n mod 2). - _Kritsada Moomuang_, Sep 06 2018
%F From _Wesley Ivan Hurt_, Apr 20 2024: (Start)
%F a(n+2) = a(n).
%F a(n+1) = a(n) + (-1)^n.
%F a(n) = (9-(-1)^n)/2. (End)
%t From _Stefano Spezia_, Sep 07 2018: (Start)
%t a[n_]:=-(1/2)*(-1)^n + 9/2; Array[a, 50, {0, 49}]
%t a[n_]:=Floor[9*(n+1)/2] - Floor[9*n/2]; Array[a, 50, {0, 49}]
%t a[n_]:= 4 + Mod[n,2]; Array[a, 50, {0, 49}]
%t LinearRecurrence[{0, 1}, {4, 5}, 50]
%t CoefficientList[Series[(4+5*x)/(1-x^2), {x, 0, 50}], x]
%t (End)
%o (PARI) a(n)=4+n%2 \\ _Jaume Oliver Lafont_, Mar 20 2009
%o (PARI) a(n) = my(v=[4, 5]); v[n%2+1] \\ _Felix Fröhlich_, Sep 06 2018
%o (PARI) Vec((4+5*x)/(1-x^2) + O(x^100)) \\ _Felix Fröhlich_, Sep 06 2018
%Y Cf. A176215.
%K nonn,easy,changed
%O 0,1
%A _N. J. A. Sloane_
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