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A095130 Expansion of (x+x^2)/(1-x^6); period 6: repeat [0, 1, 1, 0, 0, 0]. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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

Table of n, a(n) for n=0..104.

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

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) = 1/90*{2*(n mod 6)+2*[(n+1) mod 6]+2*[(n+2) mod 6]+17*[(n+3) mod 6]+2*[(n+4) mod 6]-13*[(n+5) mod 6]} with n>=0. - Paolo P. Lava, Nov 27 2006

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

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 *)

PROG

(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

CROSSREFS

Cf. A011658, A095129.

Sequence in context: A194685 A182582 A125720 * A284789 A288736 A270803

Adjacent sequences:  A095127 A095128 A095129 * A095131 A095132 A095133

KEYWORD

easy,nonn

AUTHOR

Paul Barry, May 29 2004

EXTENSIONS

Corrected by T. D. Noe, Nov 08 2006

STATUS

approved

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Last modified January 22 16:29 EST 2020. Contains 331152 sequences. (Running on oeis4.)