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 A099782 #11 Sep 08 2022 08:45:15
%S A099782 1,4,16,66,280,1216,5380,24144,109504,500488,2300128,10612224,
%T A099782 49096720,227578432,1056304384,4907373600,22813275520,106100835328,
%U A099782 493609021504,2296885357824,10689540189184,49753373831296,231588118339072
%N A099782 a(n) = Sum_{k=0..floor(n/3)} C(n-k,2*k) * 2^k * 4^(n-3*k).
%C A099782 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 A099782 G. C. Greubel, <a href="/A099782/b099782.txt">Table of n, a(n) for n = 0..1000</a>
%H A099782 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (8,-16,2).
%F A099782 G.f.: (1-4*x)/((1-4*x)^2 - 2*x^3).
%F A099782 a(n) = 8*a(n-1) - 16*a(n-2) + 2*a(n-3).
%p A099782 seq(coeff(series((1-4*x)/((1-4*x)^2 - 2*x^3), x, n+1), x, n), n = 0 .. 40); # _G. C. Greubel_, Sep 04 2019
%t A099782 LinearRecurrence[{8,-16,2}, {1,4,16}, 30] (* _G. C. Greubel_, Sep 04 2019 *)
%o A099782 (PARI) my(x='x+O('x^30)); Vec((1-4*x)/((1-4*x)^2 - 2*x^3)) \\ _G. C. Greubel_, Sep 04 2019
%o A099782 (Magma) I:=[1,4,16]; [n le 3 select I[n] else 8*Self(n-1) - 16*Self(n-2) + 2*Self(n-3): n in [1..30]]; // _G. C. Greubel_, Sep 04 2019
%o A099782 (Sage)
%o A099782 def A099782_list(prec):
%o A099782 P.<x> = PowerSeriesRing(ZZ, prec)
%o A099782 return P((1-4*x)/((1-4*x)^2 - 2*x^3)).list()
%o A099782 A099782_list(30) # _G. C. Greubel_, Sep 04 2019
%o A099782 (GAP) a:=[1,4,16];; for n in [4..30] do a[n]:=8*a[n-1]-16*a[n-2] + 2*a[n-3]; od; a; # _G. C. Greubel_, Sep 04 2019
%Y A099782 Cf. A099780, A099781, A099783, A099784, A099785, A099786, A099787.
%K A099782 easy,nonn
%O A099782 0,2
%A A099782 _Paul Barry_, Oct 26 2004