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Search: id:A007910
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| A007910 |
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G.f.: 1/((1-2*x)*(1+x^2)). |
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+0
6
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| 1, 2, 3, 6, 13, 26, 51, 102, 205, 410, 819, 1638, 3277, 6554, 13107, 26214, 52429, 104858, 209715, 419430, 838861, 1677722, 3355443, 6710886, 13421773, 26843546, 53687091, 107374182, 214748365, 429496730, 858993459, 1717986918, 3435973837, 6871947674
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(n)=2a(n-1)-a(n-2)+2a(n-3). Sequence is identical to its half second differences from the second term; a(n)+a(n+2)=2^(n+2). - Paul Curtz (bpcrtz(AT)free.fr), Dec 17 2007
Also describes the location a(n) of the minimal scaling factor when rescaling an FFT of order 2^{n+2} in order to (currently) minimize the arithmetic operation count (Johnson & Frigo, 2007). - Steven G. Johnson (stevenj(AT)math.mit.edu), Dec 27 2006
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REFERENCES
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I. Gessel, Problem 10424, Amer. Math. Monthly, 102 (1995), 70.
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LINKS
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S. G. Johnson and M. Frigo, A modified split-radix FFT with fewer arithmetic operations, IEEE Trans. Signal Processing 55 (2007), 111-119.
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FORMULA
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a(1) = 1, a(2n+1) = 2*a(2n) and a(2n) = 2*a(2n-1) + (-1)^n.
a(n) = (4*2^n+cos(pi*n/2)+2sin(pi*n/2))/5. - Paul Barry (pbarry(AT)wit.ie), Dec 17 2003
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CROSSREFS
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Sequence in context: A018775 A086514 A079662 this_sequence A052702 A058766 A127601
Adjacent sequences: A007907 A007908 A007909 this_sequence A007911 A007912 A007913
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KEYWORD
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nonn,easy
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AUTHOR
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Mogens Esrom Larsen (mel(AT)math.ku.dk)
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EXTENSIONS
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Entry revised Feb 24 2004 - njas
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