OFFSET
0,3
COMMENTS
A Chebyshev transform of the sequence 1,1,3,9,27 with g.f. (1-2x)/(1-3x). The image of G(x) under the Chebyshev transform is (1/(1+x^2))G(x/(1+x^2)).
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-2,3,-1).
FORMULA
a(n)=3a(n-1)-2a(n-2)+3a(n-3);
a(n)=sum{k=0..floor(n/2), binomial(n-k, k)(-1)^n*(3^(n-2k)+2*0^(n-2k))/3};
a(n)=sum{k=0..n, (0^k-2sin(pi*k/2))F(2(n-k)+2)}.
(1/3) [Fib(2n+2) + I^n + (-I)^n ]. - Ralf Stephan, Dec 04 2004
MATHEMATICA
LinearRecurrence[{3, -2, 3, -1}, {1, 1, 2, 7}, 40] (* Harvey P. Dale, Mar 25 2020 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Oct 18 2004
STATUS
approved