|
Search: id: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, 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, 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
(list; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
COMMENT
|
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)lhsystems.com), Jun 01 2005
|
|
LINKS
|
Tanya Khovanova, Recursive Sequences
Ralph E. Griswold, Shaft Sequences
|
|
FORMULA
|
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
|
|
CROSSREFS
|
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)
Adjacent sequences: A061344 A061345 A061346 this_sequence A061348 A061349 A061350
Sequence in context: A057079 A087204 A131534 this_sequence A115579 A115573 A115578
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
Jason Earls (jcearls(AT)cableone.net), Jun 07 2001
|
|
|
Search completed in 0.004 seconds
|
