|
|
A099858
|
|
A Chebyshev transform of (1+3x)/(1-3x).
|
|
3
|
|
|
1, 6, 17, 42, 109, 288, 755, 1974, 5167, 13530, 35423, 92736, 242785, 635622, 1664081, 4356618, 11405773, 29860704, 78176339, 204668310, 535828591, 1402817466, 3672623807, 9615053952, 25172538049, 65902560198, 172535142545
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
The g.f. is related to the g.f. of A099856 by the Chebyshev mapping G(x)-> (1/(1+x^2))G(x/(1+x^2)).
|
|
LINKS
|
|
|
FORMULA
|
G.f.: (1+3x+x^2)/((1+x^2)(1-3x+x^2)); a(n)=sum{k=0..floor(n/2), binomial(n-k, k)(-1)^k*(6*3^(n-2k-1)-0^(n-2k)}; a(n)=sum{k=0..n, (0^k+6*Fib(2k))cos(pi*(n-k)/2)}; a(n)=sum{k=0..n, A099857(k)*cos(pi*(n-k)/2)}; a(n)=3a(n-1)-2a(n-2)+3a(n-3)-a(n-4).
(1/2) [4Fib(2n+2) - I^n - (-I)^n ]. - Ralf Stephan, Dec 04 2004
|
|
MATHEMATICA
|
LinearRecurrence[{3, -2, 3, -1}, {1, 6, 17, 42}, 40] (* Harvey P. Dale, Apr 17 2024 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn,changed
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|