login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A259044 Period 8 sequence [ 0, 1, 0, 1, 1, 1, 0, 1, ...]. 1
0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..86.

M. Somos, Rational Function Multiplicative Coefficient

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

FORMULA

Euler transform of length 8 sequence [ 0, 1, 1, 0, -1, -1, 0, 1].

Moebius transform is length 8 sequence [ 1, -1, 0, 1, 0, 0, 0, -1].

a(n) is multiplicative with a(2) = 0, a(4) = 1, a(2^e) = 0 if e>2, a(p^e) = 1 if p>2.

G.f.: x * (1 - x^5) * (1 + x^3) / ((1 - x^2) * (1 - x^8)).

G.f.: x * (1 - x^5) * (1 - x^6) / ((1 - x^2) * (1 - x^3) * (1 - x^8)).

G.f.: f(x) + f(x^4) where f(x) := x / (1 - x^2).

a(n) = a(-n) = a(n+8) for all n in Z.

a(n) = -(-1)^n * A280237(n). a(2*n + 1) = 1. a(4*n + 2) = 0.

G.f.: -x*(x^2-x+1)*(x^4+x^3+x^2+x+1) / ( (x-1)*(1+x)*(x^2+1)*(x^4+1) ). - R. J. Mathar, Jun 18 2015

EXAMPLE

G.f. = x + x^3 + x^4 + x^5 + x^7 + x^9 + x^11 + x^12 + x^13 + x^15 + ...

MATHEMATICA

a[ n_] := Mod[n, 2] + Boole[Mod[n, 8] == 4];

a[ n_] := { 1, 0, 1, 1, 1, 0, 1, 0}[[Mod[n, 8, 1]]];

a[ n_] := SeriesCoefficient[ x / (1 - x^2) + x^4 / (1 - x^8), {x, 0, Abs@n}];

PadRight[{}, 120, {0, 1, 0, 1, 1, 1, 0, 1}] (* Harvey P. Dale, Feb 22 2018 *)

PROG

(PARI) {a(n) = (n%2) + (n%8==4)};

(PARI) {a(n) = [ 0, 1, 0, 1, 1, 1, 0, 1][n%8 + 1]};

(PARI) {a(n) = polcoeff( x / (1 - x^2) + x^4 / (1 - x^8) + x * O(x^abs(n)), abs(n))};

CROSSREFS

Cf. A280237.

Sequence in context: A023532 A030308 A280237 * A112690 A115971 A072165

Adjacent sequences:  A259041 A259042 A259043 * A259045 A259046 A259047

KEYWORD

nonn,mult,easy

AUTHOR

Michael Somos, Jun 17 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified May 20 17:45 EDT 2018. Contains 304340 sequences. (Running on oeis4.)