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 A099781 #11 Sep 08 2022 08:45:15
%S A099781 1,4,16,65,268,1120,4737,20244,87280,379073,1656348,7272896,32060673,
%T A099781 141775396,628505296,2791696705,12419264300,55315472416,246607247233,
%U A099781 1100229683508,4911436984752,21934428189121,97992663440444
%N A099781 a(n) = Sum_{k=0..floor(n/3)} C(n-k,2*k) * 4^(n-3*k).
%C A099781 In general a(n) = Sum_{k=0..floor(n/3)} C(n-k,2*k) * u^k * v^(n-3*k) has g.f. (1-v*x)/((1-v*x)^2 - u*x^2) and satisfies the recurrence a(n) = 2*u*v*a(n-1) - v^2*a(n-2) + u*a(n-3).
%H A099781 G. C. Greubel, <a href="/A099781/b099781.txt">Table of n, a(n) for n = 0..1000</a>
%H A099781 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (8,-16,1).
%F A099781 G.f.: (1-4*x)/((1-4*x)^2 - x^3).
%F A099781 a(n) = 8*a(n-1) - 16*a(n-2) + a(n-3).
%p A099781 seq(coeff(series((1-4*x)/((1-4*x)^2 -x^3), x, n+1), x, n), n = 0..30); # _G. C. Greubel_, Sep 04 2019
%t A099781 LinearRecurrence[{8,-16,1},{1,4,16},30] (* _Harvey P. Dale_, Jul 07 2013 *)
%o A099781 (PARI) my(x='x+O('x^30)); Vec((1-4*x)/((1-4*x)^2 -x^3)) \\ _G. C. Greubel_, Sep 04 2019
%o A099781 (Magma) I:=[1,4,16]; [n le 3 select I[n] else 8*Self(n-1) - 16*Self(n-2) + Self(n-3): n in [1..30]];
%o A099781 (Sage)
%o A099781 def A099781_list(prec):
%o A099781 P.<x> = PowerSeriesRing(ZZ, prec)
%o A099781 return P((1-4*x)/((1-4*x)^2 -x^3)).list()
%o A099781 A099781_list(30) # _G. C. Greubel_, Sep 04 2019
%o A099781 (GAP) a:=[1,4,16];; for n in [4..30] do a[n]:=8*a[n-1]-16*a[n-2]+a[n-3]; od; a; # _G. C. Greubel_, Sep 04 2019
%K A099781 easy,nonn
%O A099781 0,2
%A A099781 _Paul Barry_, Oct 26 2004