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 A274638 #19 Oct 21 2024 08:59:28
%S A274638 0,0,3,5,15,27,63,119,255,495,1023,2015,4095,8127,16383,32639,65535,
%T A274638 130815,262143,523775,1048575,2096127,4194303,8386559,16777215,
%U A274638 33550335,67108863,134209535,268435455,536854527,1073741823,2147450879,4294967295,8589869055,17179869183,34359607295,68719476735
%N A274638 Main diagonal of A274637.
%H A274638 Colin Barker, <a href="/A274638/b274638.txt">Table of n, a(n) for n = 0..1000</a>
%H A274638 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,0,-6,4).
%F A274638 From _Colin Barker_, Jul 09 2016: (Start)
%F A274638 a(n) = (-1+2^n+2^((n-3)/2)*(-1+(-1)^n)).
%F A274638 a(n) = 2^n-1 for n even.
%F A274638 a(n) = 2^n-1-2^((n-1)/2) for n odd.
%F A274638 a(n) = 3*a(n-1)-6*a(n-3)+4*a(n-4) for n>3.
%F A274638 G.f.: x^2*(3-4*x) / ((1-x)*(1-2*x)*(1-2*x^2)).
%F A274638 (End)
%t A274638 LinearRecurrence[{3, 0, -6, 4}, {0, 0, 3, 5}, 50] (* _Paolo Xausa_, Oct 21 2024 *)
%o A274638 (PARI) concat([0,0], Vec(x^2*(3-4*x)/((1-x)*(1-2*x)*(1-2*x^2)) + O(x^40))) \\ _Colin Barker_, Jul 09 2016
%Y A274638 Cf. A274637.
%K A274638 nonn,easy
%O A274638 0,3
%A A274638 _N. J. A. Sloane_, Jul 08 2016