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Search: id:A099858
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| A099858 |
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A Chebyshev transform of (1+3x)/(1-3x). |
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+0
3
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| 1, 6, 17, 42, 109, 288, 755, 1974, 5167, 13530, 35423, 92736, 242785, 635622, 1664081, 4356618, 11405773, 29860704, 78176339, 204668310, 535828591, 1402817466, 3672623807, 9615053952, 25172538049, 65902560198, 172535142545
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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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)).
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FORMULA
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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
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CROSSREFS
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Sequence in context: A101945 A013319 A047861 this_sequence A062020 A066183 A048746
Adjacent sequences: A099855 A099856 A099857 this_sequence A099859 A099860 A099861
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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 28 2004
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