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A099483
A Fibonacci convolution.
4
0, 1, 3, 7, 18, 48, 126, 329, 861, 2255, 5904, 15456, 40464, 105937, 277347, 726103, 1900962, 4976784, 13029390, 34111385, 89304765, 233802911, 612103968, 1602508992, 4195423008, 10983760033, 28755857091, 75283811239, 197095576626
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)).
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