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 A193884 #18 Apr 07 2024 08:49:18
%S A193884 1,1,0,0,-1,-2,-2,-2,-1,1,3,5,6,5,2,-3,-9,-14,-16,-13,-4,10,26,39,43,
%T A193884 33,7,-32,-75,-108,-115,-83,-8,100,215,298,306,206,-9,-307,-613,-819,
%U A193884 -810,-503,110,929,1739,2242,2132,1203,-536,-2778,-4910,-6113,-5577
%N A193884 Expansion of o.g.f. (1-x^2)/(1-x+x^4).
%C A193884 The Kn11 sums, see A180662, of triangle A108299 equal the terms of this sequence.
%H A193884 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,-1).
%F A193884 G.f.: (1+x)*(1-x)/(1-x+x^4).
%F A193884 a(n) = a(n-1)-a(n-4), a(0) = a(1) = 1, a(2) = a(3) = 0.
%F A193884 a(n) = A099530(n) - A099530(n-2).
%p A193884 A193884 := proc(n) option remember: if n=0 then 1 elif n=1 then 1 elif n=2 then 0 elif n=3 then 0 elif n>=4 then procname(n-1)-procname(n-4) fi: end: seq(A193884(n), n=0..54);
%t A193884 CoefficientList[Series[(1-x^2)/(1-x+x^4),{x,0,80}],x] (* or *) LinearRecurrence[{1,0,0,-1},{1,1,0,0},80] (* _Harvey P. Dale_, Jul 15 2020 *)
%Y A193884 Cf. A099530, A108299, A180662.
%K A193884 sign,easy
%O A193884 0,6
%A A193884 _Johannes W. Meijer_, Aug 11 2011