0,1

A binary m-sequence: expansion of reciprocal of x^2+x+1 (mod 2).

A Chebyshev transform of the Jacobsthal numbers A001045: if A(x) is the g.f. of a sequence, map it to ((1-x^2)/(1+x^2))A(x/(1+x^2)). - Paul Barry (pbarry(AT)wit.ie), Feb 16 2004

This is the r=1 member of the r-family of sequences S_r(n) defined in A092184 where more information can be found.

This is the Fibonacci sequence (A00045) modulo 2. - Stephen Jordan (sjordan(AT)mit.edu), Sep 10 2007

For n>0: a(n) = A084937(n-1) mod 2. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Dec 16 2007

This is also the Lucas numbers (A000032) mod 2. In general, this is the parity of any Lucas sequence associated with any pair (P,Q) when P and Q are odd; i.e., a(n) = U_n(P,Q) mod 2 = V_n(P,Q) mod 2. See Ribenboim. [From Rick L. Shepherd (rshepherd2(AT)hotmail.com), Feb 07 2009]

Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), May 04 2009: (Start)

Starting with offset 1: (1, 1, 0, 1, 1, 0,...) = INVERTi transform of the

Tribonacci sequence A001590 starting (1, 2, 3, 6, 11, 20, 37,...). (End)

n^6 mod 3. [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 06 2009]

S. W. Golomb, Shift-Register Sequences, Holden-Day, San Francisco, 1967.

H. D. Lueke, Korrelationssignale, Springer 1992, pp. 43-48.

F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.

P. Ribenboim, The Little Book of Big Primes. Springer-Verlag, NY, 1991, p. 46. [From Rick L. Shepherd (rshepherd2(AT)hotmail.com), Feb 07 2009]

Index entries for two-way infinite sequences

Index entries for sequences related to linear recurrences with constant coefficients

Index entries for characteristic functions

Index entries for sequences related to Chebyshev polynomials.

G.f.: (x+x^2)/(1-x^3) = Sum_{n>0} x^n-x^(3n). a(n)=a(n-3)=a(-n).

a(n)=(1/2)((-1)^(Floor[(2n + 4)/3]) + 1). - Mario Catalani (mario.catalani(AT)unito.it), Oct 22 2003

a(n)=mod(Fib(n), 2) - Paul Barry (pbarry(AT)wit.ie), Nov 12 2003

a(n) = 2/3*(1-cos(2Pi*n/3)). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Jan 06 2004

a(n)=1-a(n-1)*a(n-2), a(n)=n for n<2. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 28 2004

a(n)= 2*(1-T(n, -1/2))/3 with Chebyshev's polynomials T(n, x) of the first kind; see A053120. W. Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Oct 18 2004

a(n)=n*sum{k=0..floor(n/2), (-1)^k*binomial(n-k, k)*A001045(n-2k)/(n-k)} - Paul Barry (pbarry(AT)wit.ie), Oct 31 2004

a(n)=mod(A002487(n), 2); - Paul Barry (pbarry(AT)wit.ie), Jan 14 2005

a(n)= n^2 mod 3 a(n)=(1/3)*(2-(r^n+r^(2*n))) where r=(-1+sqrt(-3))/2 (closed form) - Bruce Corrigan (scentman(AT)myfamily.com), Aug 08 2005

Euler transform of length 3 sequence [1, -1, 1]. - Michael Somos Sep 23 2005

Moebius transform is length 3 sequence [1, 0, -1]. - Michael Somos Sep 23 2005

Multiplicative with a(3^e) = 0^e, a(p^e) = 1 otherwise. - Michael Soos Sep 23 2005

a(n)={(2/3)*[cos(2*n*Pi/3)+1/2]-1}^2 - Paolo P. Lava (ppl(AT)spl.at), Oct 09 2006

a(n)=(1/9)*{5*(n mod 3)+2*[(n+1) mod 3]-[(n+2) mod 3]} with n>=0 - Paolo P. Lava (ppl(AT)spl.at), Jan 22 2007

a(n)=(4/3)*(|sin(pi*(n-2)/3)|+|sin(pi*(n-1)/3)|)*|sin(pi*n/3)|. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 27 2007

a(n)=((n+1) mod 3 + 1) mod 2 = (1-(-1)^(n-3*floor((n+1)/3)))/2. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Jun 27 2007

a(n) = 2 - a(n-1) - a(n-2) for n>1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 13 2008

a(2*n+1) = a(n+1) XOR a(n), a(2*n) = a(n), a(1) = 1, a(0) = 0. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Dec 27 2008]

(PARI) a(n)=sign(n%3)

(PARI) a(n)=!!(n%3) [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Mar 24 2009]

(Other) sage: [power_mod(n, 6, 3)for n in xrange(0, 101)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 06 2009]

Partial sums of A057078 give A011655(n+1). Cf. A049347.

A002487. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Dec 27 2008]

A001590 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), May 04 2009]

Sequence in context: A082410 A094217 A092220 this_sequence A102283 A128834 A022928

Adjacent sequences: A011652 A011653 A011654 this_sequence A011656 A011657 A011658

nonn,mult,new

N. J. A. Sloane (njas(AT)research.att.com).

More terms from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 13 2008