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 A108485 #14 May 10 2024 10:59:00
%S A108485 1,2,6,32,140,600,2632,11520,50320,219936,961376,4201984,18366144,
%T A108485 80275840,350873728,1533616128,6703206656,29298713088,128060286464,
%U A108485 559732334592,2446506216448,10693312305152,46738866751488
%N A108485 a(n) = Sum_{k=0..floor(n/2)} binomial(2n-2k,2k)2^(n-k).
%C A108485 In general, Sum_{k=0..floor(n/2)} C(2n-2k,2k)a^k*b^(n-k) has expansion (1-bx-abx^2)/(1-2bx-(2ab-b^2)x^2-2ab^2*x^3+(ab)^2*x^4).
%H A108485 Vincenzo Librandi, <a href="/A108485/b108485.txt">Table of n, a(n) for n = 0..1000</a>
%H A108485 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,0,8,-4).
%F A108485 G.f.: (1-2x-2x^2)/(1-4x-8x^3+4x^4).
%F A108485 a(n) = 4a(n-1)+8a(n-3)-4a(n-4).
%t A108485 LinearRecurrence[{4,0,8,-4},{1,2,6,32},40] (* or *) CoefficientList[Series[(1-2x-2x^2)/(1-4x-8x^3+4x^4),{x,0,40}],x] (* _Vincenzo Librandi_, Jun 26 2012 *)
%o A108485 (Magma) I:=[1, 2, 6, 32]; [n le 4 select I[n] else 4*Self(n-1)+8*Self(n-3)-4*Self(n-4): n in [1..30]]; // _Vincenzo Librandi_. Jun 26 2012
%K A108485 easy,nonn
%O A108485 0,2
%A A108485 _Paul Barry_, Jun 04 2005