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
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
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
AUTHOR
Paul Barry, Oct 28 2004
STATUS
approved