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A007910
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G.f.: 1/((1-2*x)*(1+x^2)).
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12
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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; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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
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
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REFERENCES
| I. Gessel, Problem 10424, Amer. Math. Monthly, 102 (1995), 70.
M. E. Larsen, Summa Summarum, A. K. Peters, Wellesley, MA, 2007; see p. 38. [From N. J. A. Sloane (njas(AT)research.att.com), Jan 29 2009]
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for sequences related to linear recurrences with constant coefficients
S. G. Johnson and M. Frigo, A modified split-radix FFT with fewer arithmetic operations, IEEE Trans. Signal Processing 55 (2007), 111-119.
Index to sequences with linear recurrences with constant coefficients, signature (2,-1,2).
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FORMULA
| 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
a(n) = round(2^(n+1)/5). [From Mircea Merca, Dec 27 2010]
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MAPLE
| V:=n->(1/5)*(2^(n-1)+2*cos(n*Pi/2)-sin(n*Pi/2)); [seq(V(n), n=0..12)];
seq(round(2^(n+1)/5), n=1..25) [From Mircea Merca, Dec 27 2010]
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MATHEMATICA
| CoefficientList[Series[1/((1 - 2 x) (1 + x^2)), {x, 0, 50}], x] (* From Vladimir Joseph Stephan Orlovsky, Jun 20 2011 *)
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PROG
| (MAGMA) [Round(2^(n+1)/5): n in [1..40]]; // Vincenzo Librandi, Jun 21 2011
(PARI) a(n)=2^(n+1)\/5 \\ Charles R Greathouse IV, Jun 21 2011
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CROSSREFS
| Cf. A007909, A007679.
Sequence in context: A018775 A086514 A079662 * A052702 A058766 A127601
Adjacent sequences: A007907 A007908 A007909 * A007911 A007912 A007913
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KEYWORD
| nonn,easy
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AUTHOR
| Mogens Esrom Larsen (mel(AT)math.ku.dk)
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EXTENSIONS
| Entry revised Feb 24 2004 - N. J. A. Sloane (njas(AT)research.att.com).
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