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 A052973 #24 Jul 02 2025 16:01:58
%S A052973 1,0,3,2,11,14,45,76,197,380,895,1838,4143,8762,19353,41496,90793,
%T A052973 195928,426811,923802,2008307,4352902,9454021,20504420,44513581,
%U A052973 96572820,209609143,454814022,987068631,2141901554,4648293425
%N A052973 Expansion of ( 1-x ) / ( 1-x-3*x^2+x^3 ).
%D A052973 Kenneth Edwards, Michael A. Allen, A new combinatorial interpretation of the Fibonacci numbers squared, Part II, Fib. Q., 58:2 (2020), 169-177.
%H A052973 Harvey P. Dale, <a href="/A052973/b052973.txt">Table of n, a(n) for n = 0..1000</a>
%H A052973 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=1045">Encyclopedia of Combinatorial Structures 1045</a>
%H A052973 <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,-1).
%F A052973 G.f.: -(-1+x)/(1-x-3*x^2+x^3)
%F A052973 Recurrence: {a(1)=0, a(0)=1, a(2)=3, a(n)-3*a(n+1)-a(n+2)+a(n+3)=0}
%F A052973 Sum(-1/74*(1-34*_alpha+9*_alpha^2)*_alpha^(-1-n), _alpha=RootOf(1-_Z-3*_Z^2+_Z^3))
%F A052973 a(n) = A125691(n)-A125691(n-1). - _R. J. Mathar_, Feb 27 2019
%p A052973 spec := [S,{S=Sequence(Prod(Union(Prod(Union(Z,Z),Sequence(Z)),Z),Z))},unlabeled ]: seq(combstruct[count ](spec,size=n), n=0..20);
%t A052973 CoefficientList[Series[(1-x)/(1-x-3x^2+x^3),{x,0,30}],x] (* or *) LinearRecurrence[{1,3,-1},{1,0,3},40] (* _Harvey P. Dale_, Sep 06 2017 *)
%K A052973 easy,nonn
%O A052973 0,3
%A A052973 encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E A052973 More terms from _James Sellers_, Jun 06 2000