A010710 Period 2: repeat [4,5].

4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4, 5, 4

Offset

0,1

Comments

Continued fraction of 2 + 2*sqrt(30)/5 = A176215. - R. J. Mathar, Nov 21 2011

Decimal expansion of 5/11. - Franklin T. Adams-Watters, Jan 25 2019

Also, a(n) is the number of binary sequences of length n+3 avoiding the subsequences 000, 001, 011, 111. For example, when n=5 the a(5)=5 sequences of length 8 are 01010101, 10101010, 01010100, 11010101, 11010100. - Miquel A. Fiol, Dec 28 2023

Links

Table of n, a(n) for n=0..80.

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

Formula

G.f.: (4+5*x)/(1-x^2). - Jaume Oliver Lafont, Mar 20 2009

a(n) = floor(9*(n+1)/2) - floor(9*n/2). - Hailey R. Olafson, Jul 17 2014

a(n) = 4 + (n mod 2). - Kritsada Moomuang, Sep 06 2018

From Wesley Ivan Hurt, Apr 20 2024: (Start)

a(n+2) = a(n).

a(n+1) = a(n) + (-1)^n.

a(n) = (9-(-1)^n)/2. (End)

Mathematica

From Stefano Spezia, Sep 07 2018: (Start)
a[n_]:=-(1/2)*(-1)^n + 9/2; Array[a, 50, {0, 49}]
a[n_]:=Floor[9*(n+1)/2] - Floor[9*n/2]; Array[a, 50, {0, 49}]
a[n_]:= 4 + Mod[n, 2]; Array[a, 50, {0, 49}]
LinearRecurrence[{0, 1}, {4, 5}, 50]
CoefficientList[Series[(4+5*x)/(1-x^2), {x, 0, 50}], x]
(End)

Prog

(PARI) a(n)=4+n%2 \\ Jaume Oliver Lafont, Mar 20 2009
(PARI) a(n) = my(v=[4, 5]); v[n%2+1] \\ Felix Fröhlich, Sep 06 2018
(PARI) Vec((4+5*x)/(1-x^2) + O(x^100)) \\ Felix Fröhlich, Sep 06 2018

Crossrefs

Cf. A176215.

Sequence in context: A063694 A242624 A068901 * A021026 A126128 A046565

Adjacent sequences: A010707 A010708 A010709 * A010711 A010712 A010713

Keyword

nonn,easy,changed

Author

N. J. A. Sloane

Status

approved