Search: id:A061347
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%I A061347
%S A061347 1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,
               2,
%T A061347 1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,
               2,
%U A061347 1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,
               2
%V A061347 1,1,-2,1,1,-2,1,1,-2,1,1,-2,1,1,-2,1,1,-2,1,1,-2,1,1,-2,1,1,-2,1,1,-2,
               1,1,-2,1,1,-2,
%W A061347 1,1,-2,1,1,-2,1,1,-2,1,1,-2,1,1,-2,1,1,-2,1,1,-2,1,1,-2,1,1,-2,1,1,-2,
               1,1,-2,1,1,-2,
%X A061347 1,1,-2,1,1,-2,1,1,-2,1,1,-2,1,1,-2,1,1,-2,1,1,-2,1,1,-2,1,1,-2,1,1,-2,
               1,1,-2,1,1,-2
%N A061347 Period 3.
%C A061347 Inverse binomial transform of A057079. - Paul Barry (pbarry(AT)wit.ie), 
               May 15 2003
%C A061347 The unsigned version, with g.f. (1+x+2x^2)/(1-x^3), has a(n)=4/3-cos(2*pi*n/
               3)/3-sqrt(3)sin(2*pi*n/3)/3=gcd(fib(n+4), fib(n+1)). - Paul Barry 
               (pbarry(AT)wit.ie), Apr 02 2004
%C A061347 a(n) = L(n-2,-1), where L is defined as in A108299; see also A010892 
               for L(n,+1). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Jun 01 2005
%C A061347 Contribution from Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Oct 
               16 2009: (Start)
%C A061347 From Taylor expansion of log(1+x+x^2) at x=1,
%C A061347 Sum_{k>=1} a(k)/k = log(3).
%C A061347 This is case n=3 of the general expression
%C A061347 Sum_{k>=1} (1-n*!(k%n))/k = log(n)
%C A061347 (End)
%H A061347 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A061347 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%H A061347 Ralph E. Griswold, <a href="http://www.cs.arizona.edu/patterns/sequences.html">
               Shaft Sequences</a>
%F A061347 a(0) = a(1) = 1; a(n)= - a(n-1) - a(n-2).
%F A061347 G.f.: (1+2x)/(1+x+x^2). a(n)=(-1)^Floor[2n/3]+((-1)^Floor[(2n-1)/3]+ 
               (-1)^Floor[(2n+1)/3])/2 - Mario Catalani (mario.catalani(AT)unito.it), 
               Jan 07 2003
%F A061347 a(n)=-(n mod 3)+(n+1) mod 3 - Paolo P. Lava (ppl(AT)spl.at), Oct 20 2006
%F A061347 a(n) = -2*cos(2*pi*n/3); - Jaume Oliver Lafont (joliverlafont(AT)gmail.com), 
               May 06 2008
%o A061347 (PARI) a(n)=1-3*!(n%3) [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), 
               Oct 16 2009]
%Y A061347 Apart from signs, same as A057079. Cf. A000045, A010892 for the rules 
               a(n) = a(n - 1) + a(n - 2), a(n) = a(n - 1) - a(n - 2). a(n) = - 
               a(n - 1) + a(n - 2) gives a signed version of Fibonacci numbers.
%Y A061347 a(n)=A057079(2n)
%Y A061347 Cf. A002391. [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), 
               Oct 16 2009]
%Y A061347 Sequence in context: A057079 A087204 A131534 this_sequence A115579 A115573 
               A152851
%Y A061347 Adjacent sequences: A061344 A061345 A061346 this_sequence A061348 A061349 
               A061350
%K A061347 sign
%O A061347 1,3
%A A061347 Jason Earls (zevi_35711(AT)yahoo.com), Jun 07 2001

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