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 A191830 #23 Jul 07 2025 20:15:14
%S A191830 0,0,2,1,4,5,10,16,28,47,80,135,228,384,646,1085,1820,3049,5102,8528,
%T A191830 14240,23755,39592,65931,109704,182400,303050,503161,834868,1384397,
%U A191830 2294290,3800080,6290788,10408679,17213696,28454415,47014380,77647104,128186062
%N A191830 Expansion of x^2*(2-3*x)/(1-x-x^2)^2.
%C A191830 a(2*n) mod 2 = 0;
%C A191830 a(4*n) mod 4 = 0;
%C A191830 a(5*n) mod 5 = 0 and a(5*n+1) mod 5 = 0;
%C A191830 a(n) = 2*A001629(n) - 3*A001629(n-1). - _Johannes W. Meijer_, Jun 27 2011
%H A191830 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-2,-1).
%F A191830 G.f.: x^2*(2-3*x)/(1-x-x^2)^2.
%F A191830 a(n) = a(n-1) + a(n-2) + A000045(n-5), a(0) = a(1) = 0.
%F A191830 a(0)=0, a(1)=0, a(2)=2, a(3)=1, a(n)=2*a(n-1)+a(n-2)-2*a(n-3)-a(n-4). - _Harvey P. Dale_, Mar 16 2015
%p A191830 A191830:= proc(n) option remember: if n<=1 then 0 else procname(n-1)+procname(n-2)+A000045(n-5) fi: end proc: with(combinat): A000045:=fibonacci: seq(A191830(n),n=0..30); # _Johannes W. Meijer_, Jun 27 2011
%t A191830 CoefficientList[Series[x^2(2-3x)/(1-x-x^2)^2,{x,0,40}],x] (* or *) LinearRecurrence[{2,1,-2,-1},{0,0,2,1},40] (* _Harvey P. Dale_, Mar 16 2015 *)
%o A191830 (PARI) a(n)=([0,1,0,0; 0,0,1,0; 0,0,0,1; -1,-2,1,2]^n*[0;0;2;1])[1,1] \\ _Charles R Greathouse IV_, Jul 06 2017
%Y A191830 Cf. A000045, A001629.
%K A191830 nonn,easy,less
%O A191830 0,3
%A A191830 _Paul Curtz_, Jun 17 2011