A110551 Period 6: repeat [1, 3, 5, 5, 3, 1].

1, 3, 5, 5, 3, 1, 1, 3, 5, 5, 3, 1, 1, 3, 5, 5, 3, 1, 1, 3, 5, 5, 3, 1, 1, 3, 5, 5, 3, 1, 1, 3, 5, 5, 3, 1, 1, 3, 5, 5, 3, 1, 1, 3, 5, 5, 3, 1, 1, 3, 5, 5, 3, 1, 1, 3, 5, 5, 3, 1, 1, 3, 5, 5, 3, 1, 1, 3, 5, 5, 3, 1, 1, 3, 5, 5, 3, 1, 1, 3, 5, 5, 3, 1, 1, 3, 5, 5, 3, 1

Offset: 0

Author

Paul Barry, Jul 26 2005

Keywords

• easy
• nonn

Comments

a(n) = A162699(n+1) (Modd 7) = A204453(A162699(n+1)), n>=0, where the nonnegative members of the seven residue classes Mod 7 (not to be confused with mod 7), called [m] for m=0..6, are given in the array A113807, if there the last row, starting with 7 is taken as class [0] after adding a 0 in front. Here only the classes [1], [3] and [5] are relevant. For Modd n residue classes see a comment on A203571. [Wolfdieter Lang, Feb 09 2012]

Continued fractions expansion of (8+sqrt(905))/29 = 1.3132144107925.. - R. J. Mathar, Mar 08 2012

Examples

			Modd 7 classes for positive odd numbers reduced mod 7: a(3)=5 because A162699(4)=9 (the fourth positive odd number not divisible by 7), and 9 is a member of the Modd 7 class [5] = {5,9,19,23,...}.
A162699: 1, 3, 5, 9, 11, 13, 15, 17, 19, 23, 25, 27,...
Modd 7:  1, 3, 5, 5,  3,  1,  1,  3,  5,  5,  3,  1,... [_Wolfdieter Lang_, Feb 09 2012]
		

Links

• Index entries for linear recurrences with constant coefficients, signature (2,-2,1).

Crossrefs

Cf. A001045, A105198, A110549, A110550, A113807, A162699, A203571, A204453.

Programs

Magma

&cat [[1, 3, 5, 5, 3, 1]^^30]; // Wesley Ivan Hurt, Jun 29 2016

Maple

A110551:=n->[1, 3, 5, 5, 3, 1][(n mod 6)+1]: seq(A110551(n), n=0..100); # Wesley Ivan Hurt, Jun 29 2016

Mathematica

PadRight[{}, 100, {1, 3, 5, 5, 3, 1}] (* Wesley Ivan Hurt, Jun 29 2016 *)

PARI

x='x+O('x^50); Vec((1+x+x^2)/((1-x)*(x^2-x+1))) \\ G. C. Greubel, Aug 31 2017

Formula

From R. J. Mathar, Oct 15 2014: (Start)

G.f.: ( 1+x+x^2 ) / ( (1-x)*(x^2-x+1) ).

a(n) = a(n-1) - a(n-2) + a(n-3) - a(n-4) + a(n-5) for n>4.

a(n) = 3 + 2*sin(Pi*n/3)/sqrt(3) - 2*cos(Pi*n/3).

a(n) = A001045(n+2) mod 6. (End)

From Wesley Ivan Hurt, Jun 29 2016: (Start)

a(n) = a(n-6) for n>5.

a(n) = 2*a(n-1) - 2*a(n-2) + a(n-3) for n>2. (End)