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 A189234 #28 Aug 21 2019 16:17:48
%S A189234 5,1,9,4,25,16,78,64,257,256,874,1013,3034,3953,10684,15229,38017,
%T A189234 58056,136338,219508,491870,824737,1782735,3083887,6484514,11489516,
%U A189234 23652443,42688039,86459608,158270401,316576903,585868009,1160673633,2166063365,4259693562
%N A189234 Expansion of (5-4*x-12*x^2+6*x^3+3*x^4)/(1-x-4*x^2+3*x^3+3*x^4-x^5).
%C A189234 (Start) Let U be the unit-primitive matrix (see [Jeffery])
%C A189234 U=U_(11,1)=
%C A189234 (0 1 0 0 0)
%C A189234 (1 0 1 0 0)
%C A189234 (0 1 0 1 0)
%C A189234 (0 0 1 0 1)
%C A189234 (0 0 0 1 1).
%C A189234 Then a(n)=Trace(U^n). (End)
%C A189234 Evidently one of a class of accelerator sequences for Catalan's constant based on traces of successive powers of a unit-primitive matrix U_(N,r) (0<r<floor(N/2)) and for which the closed-form expression for a(n) is derived from the eigenvalues of U_(N,r).
%H A189234 Michael De Vlieger, <a href="/A189234/b189234.txt">Table of n, a(n) for n = 0..3532</a>
%H A189234 A. Akbary, Q. Wang, <a href="http://dx.doi.org/10.1090/S0002-9939-05-08220-1">A generalized Lucas sequence and permutation binomials</a>, Proc. Amer. Math. Soc. 134 (2006) 15-22, sequence a(n) with l=11.
%H A189234 L. E. Jeffery, <a href="/wiki/User:L._Edson_Jeffery/Unit-Primitive_Matrices">Unit-primitive matrices</a>
%H A189234 Genki Shibukawa, <a href="https://arxiv.org/abs/1907.00334">New identities for some symmetric polynomials and their applications</a>, arXiv:1907.00334 [math.CA], 2019.
%H A189234 Q. Wang, <a href="https://www.semanticscholar.org/paper/On-generalized-Lucas-sequences-Wang-Akbari/7e33b3b79703dc6790fca133e8c92cc0cafcfe4a">On generalized Lucas sequences</a>, Contemp. Math. 531 (2010) 127-141, Table 1 (k=5).
%H A189234 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,4,-3,-3,1).
%F A189234 G.f.: (5-4*x-12*x^2+6*x^3+3*x^4)/(1-x-4*x^2+3*x^3+3*x^4-x^5).
%F A189234 a(n)=a(n-1)+4*a(n-2)-3*a(n-3)-3*a(n-4)+a(n-5), {a(m)}={5,1,9,4,25}, m=0..4.
%F A189234 a(n)=Sum_{k=1..5} (x_k)^n; x_k=2*(-1)^(k-1)*cos(k*Pi/11).
%t A189234 CoefficientList[Series[(5-4x-12x^2+6x^3+3x^4)/(1-x-4x^2+3x^3+ 3x^4-x^5),{x,0,40}],x] (* or *) LinearRecurrence[{1,4,-3,-3,1},{5,1,9,4,25},40] (* _Harvey P. Dale_, Jan 18 2012 *)
%o A189234 (PARI) Vec((5-4*x-12*x^2+6*x^3+3*x^4)/(1-x-4*x^2+3*x^3+3*x^4-x^5)+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012
%Y A189234 A189235, A189236, A189237.
%Y A189234 Unsigned version of A094650.
%K A189234 nonn,easy
%O A189234 0,1
%A A189234 _L. Edson Jeffery_, Apr 18 2011