This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A049602 #27 Jul 07 2017 13:59:06
%S A049602 0,1,1,5,9,30,68,195,483,1309,3355,8900,23112,60813,158717,416325,
%T A049602 1088661,2852242,7463884,19546175,51163695,133962621,350695511,
%U A049602 918170280,2403740304,6293172025,16475579353,43133883845,112925557953
%N A049602 a(n) = (Fibonacci(2*n)-(-1)^n*Fibonacci(n))/2.
%C A049602 A049602 gives the coefficients of x in the reduction of the polynomial p(n,x)=(1/2)((x+1)^n+(x-1)^n) by x^2->x+1. For the constant terms, see A192352. For an introduction to reductions of polynomials by substitutions such as x^2->x+1, see A192232. - _Clark Kimberling_, Jun 29 2011
%H A049602 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,3,-4,1).
%F A049602 a(n)=Sum{T(2i+1, n-2i-1): i=0, 1, ..., [ (n+1)/2 ]}, array T as in A049600.
%F A049602 Cosh transform of Fibonacci numbers A000045 (or mean of binomial and inverse binomial transforms of A000045). E.g.f.: cosh(x)(2/sqrt(5))*exp(x/2)*sinh(sqrt(5)*x/2). - _Paul Barry_, May 10 2003
%F A049602 a(n)=sum{k=0..floor(n/2), C(n, 2k)Fib(n-2k)}; - _Paul Barry_, May 01 2005
%F A049602 a(n)=2a(n-1)+3a(n-2)-4a(n-3)+a(n-4). - _Paul Curtz_, Jun 16 2008
%F A049602 G.f.: x(1-x)/((1+x-x^2)(1-3x+x^2)); a(n)=sum{k=0..n-1, (-1)^(n-k+1)*F(2k+2)*F(n-k+1)}; - _Paul Barry_, Jul 11 2008
%t A049602 LinearRecurrence[{2,3,-4,1},{0,1,1,5},30] (* _Harvey P. Dale_, Jul 07 2017 *)
%o A049602 (PARI) a(n)=(fibonacci(2*n)-(-1)^n*fibonacci(n))/2 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A049602 Cf. A049601.
%K A049602 nonn,easy
%O A049602 0,4
%A A049602 _Clark Kimberling_
%E A049602 Simpler description from _Vladeta Jovovic_ and _Thomas Baruchel_, Aug 24 2004
%E A049602 More terms from _Paul Curtz_, Jun 16 2008