OFFSET
0,3
COMMENTS
A Chebyshev transform of the sequence 0,1,3,9,27 with g.f. x/(1-3x). The image of G(x) under the Chebyshev transform is (1/(1+x^2))G(x/(1+x^2)).
LINKS
Index entries for linear recurrences with constant coefficients, signature (3,-2,3,-1).
FORMULA
G.f.: x/((1+x^2)(1-3x+x^2)); a(n)=3a(n-1)-2a(n-2)+3a(n-3); a(n)=sum{k=0..n, cos(pi*k/2)F(2(n-k))}. a(n)=sum{k=0..floor(n/2), binomial(n-k, k)(-1)^n*(3^(n-2k)-0^(n-2k))/3}.
(1/6) [2Fib(2n+2) - I^n - (-I)^n ]. - Ralf Stephan, Dec 04 2004
MATHEMATICA
LinearRecurrence[{3, -2, 3, -1}, {0, 1, 3, 7}, 30] (* Harvey P. Dale, May 23 2016 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Oct 18 2004
STATUS
approved