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 A161498 #24 Sep 08 2022 08:45:45
%S A161498 1,13,132,1261,11809,109824,1018849,9443629,87504516,810723277,
%T A161498 7510988353,69584925696,644660351425,5972359368781,55329992188548,
%U A161498 512595960817837,4748863783286881,43995092132369664,407585519020921249
%N A161498 Expansion of x*(1-x)*(1+x)/(1-13*x+36*x^2-13*x^3+x^4).
%C A161498 Proposed by R. Guy in the seqfan list, Mar 29 2009.
%C A161498 The sequence is the case P1 = 13, P2 = 34, Q = 1 of the 3 parameter family of 4th-order linear divisibility sequences found by Williams and Guy. - _Peter Bala_, Apr 03 2014
%H A161498 Vincenzo Librandi, <a href="/A161498/b161498.txt">Table of n, a(n) for n = 1..1000</a>
%H A161498 H. C. Williams and R. K. Guy, <a href="http://dx.doi.org/10.1142/S1793042111004587">Some fourth-order linear divisibility sequences</a>, Intl. J. Number Theory 7 (5) (2011) 1255-1277.
%H A161498 H. C. Williams and R. K. Guy, <a href="http://www.emis.de/journals/INTEGERS/papers/a17self/a17self.pdf">Some Monoapparitic Fourth Order Linear Divisibility Sequences</a> Integers, Volume 12A (2012) The John Selfridge Memorial Volume
%H A161498 <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (13,-36,13,-1)
%F A161498 a(n) = A139400(n) / ( A001906(n)*A001353(n)*A004254(n) ).
%F A161498 a(n) = 13*a(n-1)-36*a(n-2)+13*a(n-3)-a(n-4).
%F A161498 a(n) = A187732(n)-A187732(n-2). - _R. J. Mathar_, Mar 18 2011
%F A161498 From _Peter Bala_, Apr 03 2014: (Start)
%F A161498 a(n) = ( T(n,alpha) - T(n,beta) )/(alpha - beta), where alpha = 1/4*(13 + sqrt(33)), beta = 1/4*(13 - sqrt(33)) and where T(n,x) denotes the Chebyshev polynomial of the first kind.
%F A161498 a(n) = U(n-1,1/2*(4 + sqrt(3) ))*U(n-1,1/2*(4 - sqrt(3))) for n >= 1, where U(n,x) denotes the Chebyshev polynomial of the second kind.
%F A161498 a(n) = bottom left entry of the 2 X 2 matrix T(n, M), where M is the 2 X 2 matrix [0, -17/2; 1, 13/2].
%F A161498 See the remarks in A100047 for the general connection between Chebyshev polynomials of the first kind and 4th-order linear divisibility sequences. (End)
%t A161498 CoefficientList[Series[(1 - x)*(1 + x)/(1 - 13*x + 36*x^2 - 13*x^3 + x^4), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 19 2012 *)
%o A161498 (Magma) I:=[1,13,132,1261]; [n le 4 select I[n] else 13*Self(n-1)-36*Self(n-2)+13*Self(n-3)-Self(n-4): n in [1..20]]; // _Vincenzo Librandi_, Dec 19 2012
%Y A161498 Cf. A006238, A100047.
%K A161498 nonn,easy
%O A161498 1,2
%A A161498 _R. J. Mathar_, Jun 11 2009