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

Offset: 0

Author

Paul Barry, Jul 26 2005

Keywords

• nonn
• easy

Comments

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

Continued fraction expansion of (337 + sqrt(905669))/890 = 1.44793981253727... - R. J. Mathar, Mar 08 2012

Links

• Antti Karttunen, Table of n, a(n) for n = 0..8191
• Index entries for linear recurrences with constant coefficients, signature (1,-1,1,-1,1,-1,1).

Crossrefs

One more than A105198.

Programs

Mathematica

PadRight[{},120,{1,2,4,3,3,4,2,1}] (* Harvey P. Dale, May 12 2015 *)

PARI

a(n)=[1,2,4,3,3,4,2,1][n%8+1] \\ Charles R Greathouse IV, Oct 16 2015

Formula

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]

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

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.

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

a(n) = 1 + (A000217(n) mod 4). - Jon E. Schoenfield, Aug 11 2017