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A184334 Period 6 sequence [ 0, 2, 2, 0, -2, -2, ...] except a(0) = 1. 4
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, -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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..90.

M. Somos, Rational Function Multiplicative Coefficients

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

FORMULA

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.

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

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

G.f.: (1 + x + x^2) / (1 - x + x^2). a(-n) = -a(n) unless n = 0. a(n+3) = -a(n) unless n = 0 or n = -3.

G.f.: 1 / (1 - 2*x / (1 + x / (1 - x / (1 + x)))). - Michael Somos, Jan 03 2013

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

3*a(n)= -(n mod 6) +[(n+2) mod 6] +[(n+3) mod 6] -[(n+5) mod 6] + 3*[binom(2*n,n) mod 2]. Paolo P. Lava, Mar 10 2011

a(n) = A257076(n-1) = A109265(n-2) if n>2. - Michael Somos, Sep 01 2015

EXAMPLE

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 + ...

MATHEMATICA

PadRight[{1}, 120, {0, 2, 2, 0, -2, -2}] (* Harvey P. Dale, Apr 02 2015 *)

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

PROG

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

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

CROSSREFS

Cf. A109265, A130772, A257076.

Sequence in context: A130772 A257076 A109265 * A225399 A035668 A215283

Adjacent sequences:  A184331 A184332 A184333 * A184335 A184336 A184337

KEYWORD

sign,easy

AUTHOR

Michael Somos, Feb 13 2011

STATUS

approved

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Last modified June 26 02:24 EDT 2017. Contains 288749 sequences.