A110549 - OEIS

%I #32 May 15 2019 06:01:22

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

%C Permutation of {1,2,3,4} followed by its reversal, repeated.

%C Continued fraction expansion of (337 + sqrt(905669))/890 = 1.44793981253727... - _R. J. Mathar_, Mar 08 2012

%H Antti Karttunen, <a href="/A110549/b110549.txt">Table of n, a(n) for n = 0..8191</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,-1,1,-1,1,-1,1).

%F 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 a(n) = a(n-1) - a(n-2) + a(n-3) - a(n-4) + a(n-5) - a(n-6) + a(n-7);

%F 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 a(n) = 1 + A105198(n).

%F a(n) = 1 + (A000217(n) mod 4). - _Jon E. Schoenfield_, Aug 11 2017

%t PadRight[{},120,{1,2,4,3,3,4,2,1}] (* _Harvey P. Dale_, May 12 2015 *)

%o (PARI) a(n)=[1,2,4,3,3,4,2,1][n%8+1] \\ _Charles R Greathouse IV_, Oct 16 2015

%Y One more than A105198.

%K nonn,easy

%O 0,2

%A _Paul Barry_, Jul 26 2005