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 A093041 #7 Feb 27 2024 18:50:08
%S A093041 1,1,2,6,16,38,86,192,426,938,2048,4438,9558,20480,43690,92842,196608,
%T A093041 415062,873814,1835008,3844778,8039082,16777216,34952534,72701270,
%U A093041 150994944,313174698,648719018,1342177280,2773833046,5726623062
%N A093041 Expansion of (1-4x+6x^2-3x^3)/(1-5x+9x^2-8x^3+4x^4).
%C A093041 Binomial transform of A008611.
%H A093041 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (5,-9,8,-4)
%F A093041 a(n)=2(cos(pi*n/3)-sqrt(3)sin(pi*n/3)/3)/3+2^n/3+n*2^(n-1)/3; a(n)=2*A010892(n+1)/3+A000079(n)/3+A001787(n)/3.
%t A093041 CoefficientList[Series[(1-4x+6x^2-3x^3)/(1-5x+9x^2-8x^3+4x^4),{x,0,30}],x] (* or *) LinearRecurrence[ {5,-9,8,-4},{1,1,2,6},40] (* _Harvey P. Dale_, Feb 27 2024 *)
%K A093041 easy,nonn
%O A093041 0,3
%A A093041 _Paul Barry_, Mar 18 2004