|
Search: id:A100047
|
|
|
| A100047 |
|
A Chebyshev transform of the Fibonacci numbers. |
|
+0
6
|
|
| 0, 1, 1, -1, -1, 0, -1, -1, 1, 1, 0, 1, 1, -1, -1, 0, -1, -1, 1, 1, 0, 1, 1, -1, -1, 0, -1, -1, 1, 1, 0, 1, 1, -1, -1, 0, -1, -1, 1, 1, 0, 1, 1, -1, -1, 0, -1, -1, 1, 1, 0, 1, 1, -1, -1, 0, -1, -1, 1, 1, 0, 1, 1, -1, -1, 0, -1, -1, 1, 1, 0, 1, 1, -1, -1, 0, -1, -1, 1, 1, 0, 1, 1, -1, -1, 0, -1, -1, 1, 1
(list; graph; listen)
|
|
|
OFFSET
|
0,1
|
|
|
COMMENT
|
Multiplicative with a(p^e) = -1^(e+1) if p = 2, 0 if p = 5, 1 if p == 1 or 9 (mod 10), -1^e if p == 3 or 7 (mod 10). David W. Wilson (davidwwilson(AT)comcast.net) Jun 10, 2005.
|
|
FORMULA
|
G.f.: x(1-x^2)/(1-x+x^2-x^3+x^4); a(n)=a(n-1)-a(n-2)+a(n-3)-a(n-4); a(n)=n*sum{k=0..floor(n/2), (-1)^k*binomial(n-k, k)A000045(n-2k)/(n-k)}.
|
|
EXAMPLE
|
A Chebyshev transform of the Fibonacci numbers A000045: if A(x) is the
g.f. of a sequence, map it to ((1-x^2)/(1+x^2))A(x/(1+x^2)).
The denominator is the 10th cyclotomic polynomial.
|
|
CROSSREFS
|
Cf. A099443, A011655, A100048.
Adjacent sequences: A100044 A100045 A100046 this_sequence A100048 A100049 A100050
Sequence in context: A092248 A106743 A011558 this_sequence A080891 A112713 A143536
|
|
KEYWORD
|
easy,sign,mult
|
|
AUTHOR
|
Paul Barry (pbarry(AT)wit.ie), Oct 31 2004
|
|
|
Search completed in 0.002 seconds
|
