A095130 Expansion of (x+x^2)/(1-x^6); period 6: repeat [0, 1, 1, 0, 0, 0].

0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1

Offset: 0

Author

Paul Barry, May 29 2004

Keywords

• easy
• nonn

Comments

Sequences of period k composed of (k-p) zeros followed by p ones have a closed formula of floor((n mod k)/(k-p)), for p>=floor(n/2). [Gary Detlefs, May 18 2011]

Links

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

Crossrefs

Cf. A011658, A095129.

Programs

Magma

[Floor(((n+3) mod 6)/4) : n in [0..100]]; // Wesley Ivan Hurt, Sep 08 2015

Magma

&cat[[0,1,1,0,0,0]: n in [0..15]]; // Vincenzo Librandi, Sep 09 2015

Maple

A095130:=n->floor(((n+3) mod 6)/4); seq(A095130(n), n=0..100); # Wesley Ivan Hurt, Feb 24 2014

Mathematica

PadRight[{},120,{0,1,1,0,0,0}] (* or *) LinearRecurrence[{1,-1,1,-1,1},{0,1,1,0,0},120] (* Harvey P. Dale, Nov 18 2013 *)

Formula

G.f.: x/(1-x+x^2-x^3+x^4-x^5);

a(n) = 1/3-cos(2*Pi*n/3)/3+sin(Pi*n/3)/sqrt(3).

a(n) = mod(A095129(n),3).

a(n) = floor(((n+3) mod 6)/4). [Gary Detlefs, May 18 2011]

a(0)=0, a(1)=1, a(2)=1, a(3)=0, a(4)=0, a(n) = a(n-1)-a(n-2)+a(n-3)-a(n-4)+ a(n-5). - Harvey P. Dale, Nov 18 2013

a(n) = floor((n-1)/6) - floor((n-3)/6). - Wesley Ivan Hurt, Sep 08 2015

Extensions

Corrected by T. D. Noe, Nov 08 2006