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A110549 Period 8: repeat [1, 2, 4, 3, 3, 4, 2, 1].

%I A110549 #32 May 15 2019 06:01:22
%S A110549 1,2,4,3,3,4,2,1,1,2,4,3,3,4,2,1,1,2,4,3,3,4,2,1,1,2,4,3,3,4,2,1,1,2,
%T A110549 4,3,3,4,2,1,1,2,4,3,3,4,2,1,1,2,4,3,3,4,2,1,1,2,4,3,3,4,2,1,1,2,4,3,
%U A110549 3,4,2,1,1,2,4,3,3,4,2,1,1,2,4,3,3,4,2,1,1,2,4,3,3,4,2,1
%N A110549 Period 8: repeat [1, 2, 4, 3, 3, 4, 2, 1].
%C A110549 Permutation of {1,2,3,4} followed by its reversal, repeated.
%C A110549 Continued fraction expansion of (337 + sqrt(905669))/890 = 1.44793981253727... - _R. J. Mathar_, Mar 08 2012
%H A110549 Antti Karttunen, <a href="/A110549/b110549.txt">Table of n, a(n) for n = 0..8191</a>
%H A110549 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,-1,1,-1,1,-1,1).
%F A110549 G.f.: (1 + x + 3*x^2 + 3*x^4 + x^5 + x^6)/(1 - x + x^2 - x^3 + x^4 - x^5 + x^6 - x^7). [corrected by _Georg Fischer_, May 15 2019]
%F A110549 a(n) = a(n-1) - a(n-2) + a(n-3) - a(n-4) + a(n-5) - a(n-6) + a(n-7);
%F A110549 a(n) = cos(3*Pi*n/4 + Pi/4)/2 + (1/2 - sqrt(2)/2)*sin(3*Pi*n/4 + Pi/4) - (1/2 + sqrt(2)/2)*cos(Pi*n/4 + Pi/4) - sin(Pi*n/4  + Pi/4)/2 - cos(Pi*n/2)/2 + sin(Pi*n/2)/2 + 5/2.
%F A110549 a(n) = 1 + A105198(n).
%F A110549 a(n) = 1 + (A000217(n) mod 4). - _Jon E. Schoenfield_, Aug 11 2017
%t A110549 PadRight[{},120,{1,2,4,3,3,4,2,1}] (* _Harvey P. Dale_, May 12 2015 *)
%o A110549 (PARI) a(n)=[1,2,4,3,3,4,2,1][n%8+1] \\ _Charles R Greathouse IV_, Oct 16 2015
%Y A110549 One more than A105198.
%K A110549 nonn,easy
%O A110549 0,2
%A A110549 _Paul Barry_, Jul 26 2005