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Search: id:A099484
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| A099484 |
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A Fibonacci convolution. |
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+0
3
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| 1, 1, 2, 7, 19, 48, 125, 329, 862, 2255, 5903, 15456, 40465, 105937, 277346, 726103, 1900963, 4976784, 13029389, 34111385, 89304766, 233802911, 612103967, 1602508992, 4195423009, 10983760033, 28755857090, 75283811239, 197095576627
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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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)).
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FORMULA
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G.f.: (1-x)^2/((1+x^2)(1-3x+x^2)); 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
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CROSSREFS
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Cf. A000045, A099483, A099485.
Sequence in context: A110299 A112304 A006589 this_sequence A018030 A051354 A073799
Adjacent sequences: A099481 A099482 A099483 this_sequence A099485 A099486 A099487
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Oct 18 2004
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