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 A099858 #19 Jan 15 2025 06:34:17
%S A099858 1,6,17,42,109,288,755,1974,5167,13530,35423,92736,242785,635622,
%T A099858 1664081,4356618,11405773,29860704,78176339,204668310,535828591,
%U A099858 1402817466,3672623807,9615053952,25172538049,65902560198,172535142545
%N A099858 A Chebyshev transform of (1+3x)/(1-3x).
%C A099858 The g.f. is related to the g.f. of A099856 by the Chebyshev mapping G(x)-> (1/(1+x^2))*G(x/(1+x^2)).
%H A099858 Harvey P. Dale, <a href="/A099858/b099858.txt">Table of n, a(n) for n = 0..1000</a>
%H A099858 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,3,-1).
%F A099858 G.f.: (1+3*x+x^2)/((1+x^2)*(1-3*x+x^2)).
%F A099858 a(n) = Sum_{k=0..floor(n/2)} binomial(n-k, k)*(-1)^k*(6*3^(n-2*k-1)-0^(n-2*k)).
%F A099858 a(n) = Sum_{k=0..n} (0^k+6*Fibonacci(2*k))*cos(Pi*(n-k)/2).
%F A099858 a(n) = Sum_{k=0..n} A099857(k)*cos(Pi*(n-k)/2).
%F A099858 a(n) = 3*a(n-1)-2*a(n-2)+3*a(n-3)-a(n-4).
%F A099858 a(n) = (1/2)*(4*Fibonacci(2*n+2) - i^n - (-i)^n). - _Ralf Stephan_, Dec 04 2004
%t A099858 LinearRecurrence[{3,-2,3,-1},{1,6,17,42},40] (* _Harvey P. Dale_, Apr 17 2024 *)
%Y A099858 Cf. A099856, A099857.
%K A099858 easy,nonn
%O A099858 0,2
%A A099858 _Paul Barry_, Oct 28 2004