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 A133993 #19 Feb 22 2020 20:07:18
%S A133993 1,2,3,4,9,14,31,56,117,226,459,908,1825,3638,7287,14560,29133,58250,
%T A133993 116515,233012,466041,932062,1864143,3728264,7456549,14913074,
%U A133993 29826171,59652316,119304657,238609286,477218599,954437168,1908874365,3817748698,7635497427
%N A133993 a(n) = a(n-1) + 3*a(n-2) - a(n-3) - 2*a(n-4), n > 3.
%H A133993 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,-1,-2).
%F A133993 a(n) = 1+4*2^n/9+(-1)^n*(n/3-4/9).
%F A133993 G.f.: ( 1+x-2*x^2-4*x^3 ) / ( (2*x-1)*(x-1)*(1+x)^2 ).
%F A133993 a(n) = 3*a(n-2) + 2*a(n-3) - 4, for n>2. - _Greg Dresden_, Feb 21 2020
%F A133993 E.g.f.: (1/9)*(4*cosh(2*x) + (13 + 3*x)*sinh(x) + cosh(x)*(5 - 3*x + 8*sinh(x))). - _Stefano Spezia_, Feb 22 2020
%t A133993 LinearRecurrence[{1,3,-1,-2},{1,2,3,4},40] (* _Harvey P. Dale_, Aug 03 2018 *)
%Y A133993 Equals 1 + A103196(n-1) for n>0. - _Greg Dresden_, Feb 21 2020
%K A133993 nonn,easy
%O A133993 0,2
%A A133993 _Paul Curtz_, Jan 22 2008
%E A133993 More terms from _Harvey P. Dale_, Aug 03 2018