cp's OEIS Frontend

A099444 A Chebyshev transform of Fib(2n+2).

%I A099444 #18 Sep 30 2018 13:14:54
%S A099444 1,3,7,15,32,69,149,321,691,1488,3205,6903,14867,32019,68960,148521,
%T A099444 319873,688917,1483735,3195552,6882329,14822619,31923791,68754951,
%U A099444 148079008,318920925,686866813,1479319737,3186042539,6861847920
%N A099444 A Chebyshev transform of Fib(2n+2).
%C A099444 The denominator is a parameterization of the Alexander polynomial for the knot 6_2 (Miller Institute knot). The g.f. is the image of the g.f. of Fib(2n+2) under the Chebyshev transform A(x)->(1/(1+x^2))A(x/(1+x^2)).
%C A099444 This sequence is the p-INVERT of A010892 using p(S) = 1 - S - S^2; see A292324.  - _Clark Kimberling_, Sep 26 2017
%H A099444 Harvey P. Dale, <a href="/A099444/b099444.txt">Table of n, a(n) for n = 0..1000</a>
%H A099444 Dror Bar-Natan, <a href="http://katlas.org/wiki/Main_Page">The Rolfsen Knot Table</a>
%H A099444 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,3,-1).
%F A099444 G.f.: (1+x^2)/(1-3x+3x^2-3x^3+x^4);
%F A099444 a(n) = sum{k=0..floor(n/2), binomial(n-k, k)(-1)^k*Fib(2(n-2k)+2)};
%F A099444 a(n) = sum{k=0..n, binomial((n+k)/2, k)(-1)^((n-k)/2)(1+(-1)^(n+k))Fib(2k+2)/2};
%F A099444 a(n) = sum{k=0..n, A099445(n-k)*binomial(1, k/2)(1+(-1)^k)/2}.
%t A099444 LinearRecurrence[{3,-3,3,-1},{1,3,7,15},30] (* _Harvey P. Dale_, Sep 30 2018 *)
%Y A099444 Cf. A001906.
%K A099444 easy,nonn
%O A099444 0,2
%A A099444 _Paul Barry_, Oct 16 2004