1,3

Inverse binomial transform of A057079. - Paul Barry (pbarry(AT)wit.ie), May 15 2003

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

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

Contribution from Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Oct 16 2009: (Start)

From Taylor expansion of log(1+x+x^2) at x=1,

Sum_{k>=1} a(k)/k = log(3).

This is case n=3 of the general expression

Sum_{k>=1} (1-n*!(k%n))/k = log(n)

(End)

Index entries for sequences related to linear recurrences with constant coefficients

Tanya Khovanova, Recursive Sequences

Ralph E. Griswold, Shaft Sequences

a(0) = a(1) = 1; a(n)= - a(n-1) - a(n-2).

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

a(n)=-(n mod 3)+(n+1) mod 3 - Paolo P. Lava (ppl(AT)spl.at), Oct 20 2006

a(n) = -2*cos(2*pi*n/3); - Jaume Oliver Lafont (joliverlafont(AT)gmail.com), May 06 2008

(PARI) a(n)=1-3*!(n%3) [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Oct 16 2009]

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.

a(n)=A057079(2n)

Cf. A002391. [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Oct 16 2009]

Sequence in context: A057079 A087204 A131534 this_sequence A115579 A115573 A152851

Adjacent sequences: A061344 A061345 A061346 this_sequence A061348 A061349 A061350

sign

Jason Earls (zevi_35711(AT)yahoo.com), Jun 07 2001