login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A184334 Period 6 sequence [0, 2, 2, 0, -2, -2, ...] except a(0) = 1. 6

%I #52 Dec 12 2023 07:40:55

%S 1,2,2,0,-2,-2,0,2,2,0,-2,-2,0,2,2,0,-2,-2,0,2,2,0,-2,-2,0,2,2,0,-2,

%T -2,0,2,2,0,-2,-2,0,2,2,0,-2,-2,0,2,2,0,-2,-2,0,2,2,0,-2,-2,0,2,2,0,

%U -2,-2,0,2,2,0,-2,-2,0,2,2,0,-2,-2,0,2,2,0,-2,-2,0,2,2,0,-2,-2,0,2,2,0,-2,-2,0

%N Period 6 sequence [0, 2, 2, 0, -2, -2, ...] except a(0) = 1.

%H G. C. Greubel, <a href="/A184334/b184334.txt">Table of n, a(n) for n = 0..2500</a>

%H Michael Somos, <a href="http://grail.eecs.csuohio.edu/rfmc.txt">Rational Function Multiplicative Coefficients</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,-1)

%F a(n) = 2 * b(n) where b() is multiplicative with b(2^e) = (-1)^(e-1) if e>0, b(3^e) = 0^e, b(p^e) = 1 if p == 1 mod 6, b(p^e) = (-1)^e if p == 5 mod 6.

%F Euler transform of length 6 sequence [2, -1, -2, 0, 0, 1].

%F G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = 2 * u * (v - 1) - (u - 1)^2 * v.

%F G.f.: (1 + x + x^2) / (1 - x + x^2).

%F a(-n) = -a(n) unless n = 0. a(n+3) = -a(n) unless n = 0 or n = -3.

%F G.f.: 1 / (1 - 2*x / (1 + x / (1 - x / (1 + x)))). - _Michael Somos_, Jan 03 2013

%F a(n) = A130772(n-1) if n>0.

%F a(n) = A257076(n-1) = A109265(n-2) if n>2. - _Michael Somos_, Sep 01 2015

%e G.f. = 1 + 2*x + 2*x^2 - 2*x^4 - 2*x^5 + 2*x^7 + 2*x^8 - 2*x^10 - 2*x^11 + ...

%t PadRight[{1},120,{0,2,2,0,-2,-2}] (* _Harvey P. Dale_, Apr 02 2015 *)

%t a[ n_] := Boole[n == 0] + {2, 2, 0, -2, -2, 0}[[Mod[n, 6, 1]]]; (* _Michael Somos_, Sep 01 2015 *)

%o (PARI) {a(n) = (n==0) + [ 0, 2, 2, 0, -2, -2][n%6+1]};

%o (PARI) {a(n) = (n==0) + 2 * (-1)^(n\3) * sign( n%3)};

%o (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1 + x+x^2)/(1-x+x^2))); // _G. C. Greubel_, Aug 04 2018

%Y Cf. A109265, A130772, A257076.

%K sign,easy

%O 0,2

%A _Michael Somos_, Feb 13 2011

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 12:26 EDT 2024. Contains 371254 sequences. (Running on oeis4.)