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 A186949 #13 Jun 29 2023 13:08:14
%S A186949 1,0,4,8,16,32,64,128,256,512,1024,2048,4096,8192,16384,32768,65536,
%T A186949 131072,262144,524288,1048576,2097152,4194304,8388608,16777216,
%U A186949 33554432,67108864,134217728,268435456,536870912,1073741824
%N A186949 a(n) = 2^n - 2*(binomial(1,n) - binomial(0,n)).
%C A186949 Binomial transform is A186948.
%C A186949 Second binomial transform is A186947.
%C A186949 Inverse binomial transform is (-1)^n * A168277(n).
%C A186949 Essentially the same as A000079, A151821, A155559, A171449, and A171559.
%H A186949 G. C. Greubel, <a href="/A186949/b186949.txt">Table of n, a(n) for n = 0..1000</a>
%H A186949 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (2).
%F A186949 G.f.: (1 - 2*x + 4*x^2)/(1-2*x).
%F A186949 a(n) = Sum_{k=0..n} binomial(n,k)*(3^k - 2*k).
%F A186949 E.g.f.: exp(2*x) - 2*x. - _G. C. Greubel_, Dec 01 2019
%p A186949 seq( `if`(n<2, 1-n, 2^n), n=0..30); # _G. C. Greubel_, Dec 01 2019
%t A186949 Table[If[n<2, 1-n, 2^n], {n, 0, 30}] (* _G. C. Greubel_, Dec 01 2019 *)
%o A186949 (PARI) vector(31, n, if(n<3, 2-n, 2^(n-1))) \\ _G. C. Greubel_, Dec 01 2019
%o A186949 (Magma) [n lt 2 select 1-n else 2^n: n in [0..30]]; // _G. C. Greubel_, Dec 01 2019
%o A186949 (Sage) [1,0]+[2^n for n in (2..30)] # _G. C. Greubel_, Dec 01 2019
%o A186949 (GAP) Concatenation([1,0], List([2..30], n-> 2^n )); # _G. C. Greubel_, Dec 01 2019
%K A186949 nonn,easy
%O A186949 0,3
%A A186949 _Paul Barry_, Mar 01 2011