Search: id:A099496
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%I A099496
%S A099496 1,2,5,13,34,89,233,610,1597,4181,10946,28657,75025,196418,514229,1346269,
%T A099496 3524578,9227465,24157817,63245986,165580141,433494437,1134903170,2971215073,
%U A099496 7778742049,20365011074,53316291173,139583862445,365435296162,956722026041
%V A099496 1,-2,5,-13,34,-89,233,-610,1597,-4181,10946,-28657,75025,-196418,514229,
               -1346269,
%W A099496 3524578,-9227465,24157817,-63245986,165580141,-433494437,1134903170,-2971215073,
%X A099496 7778742049,-20365011074,53316291173,-139583862445,365435296162,-956722026041
%N A099496 (-1)^n*Fib(2n+1).
%C A099496 With interpolated zeros, a Chebyshev transform of A056594, which has 
               g.f. 1/(1+x^2). The image of G(x) under the Chebyshev transform is 
               (1/(1+x^2))G(x/(1+x^2)).
%H A099496 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A099496 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/
               RecursiveSequences.html">Recursive Sequences</a>
%F A099496 G.f.: (1+x)/(1+3x+x^2);(with interpolated zeros) (1+x^2)/(1+3x^2+x^4); 
               a(n)=sum{k=0..floor(n/2), binomial(n-k, k)(-1)^k*cos((n-2k)*pi/2)} 
               (with interpolated zeros); a(n)=F(n+1)(-1)^(n/2)(1+(-1)^n)/2 (with 
               interpolated zeros).
%F A099496 a(n)=[(-1)^n]*[Sum{k=0..n+1}(binomial(n+k,n-k)], with n>=0 - Paolo P. 
               Lava (ppl(AT)spl.at), Apr 13 2007
%F A099496 a(n)=-3*a(n-1)-a(n-2),a(0)=1, a(1)=-2. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Nov 03 2008]
%t A099496 lst={}; Do[AppendTo[lst,(-1)^n*Fibonacci[2*n+1]],{n,5!}]; lst [From Vladimir 
               Orlovsky (4vladimir(AT)gmail.com), Jan 18 2009]
%Y A099496 Sequence in context: A122367 A001519 A048575 this_sequence A114299 A112842 
               A097417
%Y A099496 Adjacent sequences: A099493 A099494 A099495 this_sequence A099497 A099498 
               A099499
%K A099496 easy,sign
%O A099496 0,2
%A A099496 Paul Barry (pbarry(AT)wit.ie), Oct 19 2004

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