OFFSET
0,3
COMMENTS
The Chebyshev transform of the second kind maps the sequence with g.f. g(x) to the sequence with g.f. (1/(1+x^2))g(x/(1+x^2)).
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,-1,2,-1)
FORMULA
MATHEMATICA
Table[Sum[(-1)^k*Binomial[n-k, k]*Fibonacci[n-2*k, 2], {k, 0, Floor[n/2]}], {n, 0, 40}] (* G. C. Greubel, Jan 14 2022 *)
PROG
(Sage) [sum((-1)^k*binomial(n-k, k)*lucas_number1(n-2*k, 2, -1) for k in (0..(n/2))) for n in (0..40)] # G. C. Greubel, Jan 14 2022
(Magma)
C<I>:= ComplexField();
[(&+[Binomial(n-k, k)*Round(I^(n-1)*Evaluate(ChebyshevU(n-2*k), -I)): k in [0..Floor(n/2)]]) : n in [0..40]]; // G. C. Greubel, Jan 14 2022
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Sep 14 2005
STATUS
approved