Search: id:A007910
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%I A007910
%S A007910 1,2,3,6,13,26,51,102,205,410,819,1638,3277,6554,13107,26214,52429,104858,
%T A007910 209715,419430,838861,1677722,3355443,6710886,13421773,26843546,53687091,
%U A007910 107374182,214748365,429496730,858993459,1717986918,3435973837,6871947674
%N A007910 G.f.: 1/((1-2*x)*(1+x^2)).
%C A007910 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
%C A007910 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
%D A007910 I. Gessel, Problem 10424, Amer. Math. Monthly, 102 (1995), 70.
%D A007910 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]
%H A007910 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A007910 S. G. Johnson and M. Frigo, <a href="http://www.fftw.org/newsplit.pdf">
               A modified split-radix FFT with fewer arithmetic operations</a>, 
               IEEE Trans. Signal Processing 55 (2007), 111-119.
%F A007910 a(1) = 1, a(2n+1) = 2*a(2n) and a(2n) = 2*a(2n-1) + (-1)^n.
%F A007910 a(n) = (4*2^n+cos(pi*n/2)+2sin(pi*n/2))/5. - Paul Barry (pbarry(AT)wit.ie), 
               Dec 17 2003
%p A007910 V:=n->(1/5)*(2^(n-1)+2*cos(n*Pi/2)-sin(n*Pi/2)); [seq(V(n),n=0..12)];
%Y A007910 Cf. A007909, A007679.
%Y A007910 Sequence in context: A018775 A086514 A079662 this_sequence A052702 A058766 
               A127601
%Y A007910 Adjacent sequences: A007907 A007908 A007909 this_sequence A007911 A007912 
               A007913
%K A007910 nonn,easy
%O A007910 1,2
%A A007910 Mogens Esrom Larsen (mel(AT)math.ku.dk)
%E A007910 Entry revised Feb 24 2004 - N. J. A. Sloane (njas(AT)research.att.com).

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