A010717 Period 2: repeat (5,6).

5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5, 6, 5

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

This is the continued fraction expansion of the constant A176320 = 5/2 + sqrt(255)/6. - R. J. Mathar, Nov 21 2011

Links

• Index entries for linear recurrences with constant coefficients, signature (0,1).

Programs

Maple

A010717:= n -> 5 + (n mod 2):
seq(A010717(n),n=0..10); # Robert Israel, Jul 17 2014

Mathematica

Table[5 + Mod[n, 2], {n, 0, 50}] (* Jinyuan Wang, Feb 26 2020 *)

PARI

contfrac(5/2+sqrt(precision(255.,150))/6) \\ Note: Depending on the chosen precision, the last term may be off by +/- 1, so it would be safer to discard it, e.g., using vecextract(...,"^-1"). - M. F. Hasler, Sep 25 2013

PARI

a(n)=n%2+5 \\ Charles R Greathouse IV, Jul 13 2016

Formula

From Vincenzo Librandi, Aug 01 2010: (Start)

a(n) = a(n-2) for n>1; a(0)=5, a(1)=6.

G.f.: (5+6*x)/((1-x)*(1+x)). (End)

a(n) = floor(11*(n+1)/2) - floor(11*n/2). - James Van Alstine, Jul 17 2014