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 A135344 #17 Feb 03 2025 18:53:07
%S A135344 1,1,1,1,5,17,53,157,469,1405,4217,12653,37961,113881,341641,1024921,
%T A135344 3074765,9224297,27672893,83018677,249056029,747168085,2241504257,
%U A135344 6724512773,20173538321,60520614961,181561844881,544685534641,1634056603925,4902169811777
%N A135344 a(n) = 3*a(n-1) - a(n-3) + 3*a(n-4), with initial values 1,1,1,1.
%H A135344 G. C. Greubel, <a href="/A135344/b135344.txt">Table of n, a(n) for n = 0..1000</a>
%H A135344 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3, 0, -1, 3).
%F A135344 3*a(n) - a(n+1) = hexaperiodic 2, 2, 2, -2, -2, -2 = 2*A130151.
%F A135344 From _Richard Choulet_, Jan 02 2008: (Start)
%F A135344 a(n) = (1/14)*3^n + (1/6)*(-1)^n + (16/21)*cos(Pi*n/3) + (8*sqrt(3)/21)*sin(Pi*n/3).
%F A135344 a(n) = (1/14)*3^n + (1/14)*[13; 11; 5; -13; -11; -5]. (End)
%F A135344 G.f.: ( -1+2*x+2*x^2+x^3 ) / ( (3*x-1)*(1+x)*(x^2-x+1) ). - _Harvey P. Dale_, Apr 15 2012
%F A135344 42*a(n) = 7*(-1)^n +8*A167380(n+3) +3^(n+1). - _R. J. Mathar_, Oct 03 2021
%t A135344 LinearRecurrence[{3,0,-1,3},{1,1,1,1},40] (* _Harvey P. Dale_, Apr 15 2012 *)
%Y A135344 Cf. A007395.
%K A135344 nonn,easy
%O A135344 0,5
%A A135344 _Paul Curtz_, Dec 06 2007