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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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=0..28.

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

Cf. A000045, A099484, A099485.

Sequence in context: A101308 A279482 A018029 * A225034 A190255 A218250

Adjacent sequences:  A099480 A099481 A099482 * A099484 A099485 A099486

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Oct 18 2004

STATUS

approved

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Last modified April 19 06:30 EDT 2019. Contains 322237 sequences. (Running on oeis4.)