|
Search: id:A011655
|
|
|
| A011655 |
|
Periodic sequence 0,1,1,... |
|
+0
26
|
|
| 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1
(list; graph; listen)
|
|
|
OFFSET
|
0,1
|
|
|
COMMENT
|
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
|
|
REFERENCES
|
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.
|
|
LINKS
|
Index entries for sequences related to Chebyshev polynomials.
|
|
FORMULA
|
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)lhsystems.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
|
|
PROGRAM
|
(PARI) a(n)=sign(n%3)
|
|
CROSSREFS
|
Partial sums of A057078 give A011655(n+1). Cf. A049347.
Adjacent sequences: A011652 A011653 A011654 this_sequence A011656 A011657 A011658
Sequence in context: A082410 A094217 A092220 this_sequence A128834 A022928 A000494
|
|
KEYWORD
|
nonn,mult
|
|
AUTHOR
|
njas
|
|
EXTENSIONS
|
More terms from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 13 2008
|
|
|
Search completed in 0.002 seconds
|
