|
Search: id:A039834
|
|
|
| A039834 |
|
a(n+2)=-a(n+1)+a(n) (signed Fibonacci numbers); or Fibonacci numbers (A000045) extended to negative indices. |
|
+0
12
|
|
| 1, 1, 0, 1, -1, 2, -3, 5, -8, 13, -21, 34, -55, 89, -144, 233, -377, 610, -987, 1597, -2584, 4181, -6765, 10946, -17711, 28657, -46368, 75025, -121393, 196418, -317811, 514229, -832040, 1346269, -2178309, 3524578, -5702887, 9227465, -14930352, 24157817
(list; graph; listen)
|
|
|
OFFSET
|
-2,6
|
|
|
COMMENT
|
Starting with (a(-1), a(0), a(1), a(2)) = (1, 0, 1, -1) gives the subsequence called the "anti-Fibonacci numbers" [see Wikipedia]. The ratio of successive anti-Fibonacci numbers converges to -1/phi. - Jonathan Vos Post (jvospost2(AT)yahoo.com), Dec 10 2006
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n=-2..500
Wikipedia, Anti-Fibonacci number.
|
|
FORMULA
|
G.f.: (1+2*x)/(1+x-x^2).
a(n-2)=Sum_{k, 0<=k<=n}(-2)^k*A055830(n,k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 18 2006
|
|
CROSSREFS
|
Cf. A000045.
Adjacent sequences: A039831 A039832 A039833 this_sequence A039835 A039836 A039837
Sequence in context: A000044 A107358 A132636 this_sequence A000045 A134805 A020695
|
|
KEYWORD
|
sign,easy,nice
|
|
AUTHOR
|
Alexander Grasser (pyropunk(AT)usa.net)
|
|
EXTENSIONS
|
Signs corrected by Len Smiley (smiley(AT)math.uaa.alaska.edu) and njas.
|
|
|
Search completed in 0.002 seconds
|
