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 A161158 #25 Sep 08 2022 08:45:45
%S A161158 1,14,161,1792,19809,218638,2412353,26614784,293628097,3239445006,
%T A161158 35739069409,394290020096,4349990523425,47991114171406,
%U A161158 529460241815169,5841251080892416,64443392518654337,710969410782059534
%N A161158 a(n) = A003696(n+1)/A001353(n+1).
%C A161158 Proposed by R. Guy in the seqfan list Mar 28 2009.
%C A161158 With an offset of 1, this sequence is the case P1 = 14, P2 = 32, Q = 1 of the 3 parameter family of 4th-order linear divisibility sequences found by Williams and Guy. - _Peter Bala_, Apr 27 2014
%H A161158 Vincenzo Librandi, <a href="/A161158/b161158.txt">Table of n, a(n) for n = 0..900</a>
%H A161158 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 A161158 H. C. Williams and R. K. Guy, <a href="https://www.emis.de/journals/INTEGERS/papers/a17self/a17self.Abstract.html">Some Monoapparitic Fourth Order Linear Divisibility Sequences</a> Integers, Volume 12A (2012) The John Selfridge Memorial Volume.
%H A161158 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (14,-34,14,-1).
%F A161158 a(n) = 14*a(n-1) -34*a(n-2) +14*a(n-3) -a(n-4).
%F A161158 G.f.: (1-x^2)/(1-14*x+34*x^2-14*x^3+x^4).
%F A161158 From _Peter Bala_, Apr 27 2014: (Start)
%F A161158 The following remarks assume an offset of 1.
%F A161158 a(n) = (1/sqrt(17))*( T(n,(7 + sqrt(17))/2) - T(n,(7 - sqrt(17))/2) ), where T(n,x) is the Chebyshev polynomial of the first kind.
%F A161158 a(n) = the bottom left entry of the 2 X 2 matrix T(n,M), where M is the 2 X 2 matrix [0, -8; 1, 7].
%F A161158 a(n) = U(n-1,1/2*(4 + sqrt(2)))*U(n-1,1/2*(4 - sqrt(2))), where U(n,x) is the Chebyshev polynomial of the second kind.
%F A161158 See the remarks in A100047 for the general connection between Chebyshev polynomials of the first kind and 4th-order linear divisibility sequences. (End)
%p A161158 seq(simplify( ChebyshevU(n, (4+sqrt(2))/2)*ChebyshevU(n, (4-sqrt(2))/2) ), n = 0 .. 20); # _G. C. Greubel_, Dec 24 2019
%t A161158 CoefficientList[Series[(1-x^2)/(1-14x+34x^2-14x^3+x^4), {x, 0, 20}], x] (* _Vincenzo Librandi_, Apr 28 2014 *)
%t A161158 Table[Simplify[ChebyshevU[n, (4+Sqrt[2])/2]*ChebyshevU[n, (4-Sqrt[2])/2]], {n, 0, 20}] (* _G. C. Greubel_, Dec 24 2019 *)
%o A161158 (Magma) I:=[1,14,161,1792]; [n le 4 select I[n] else 14*Self(n-1)-34*Self(n-2) +14*Self(n-3)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Apr 28 2014
%o A161158 (PARI) vector(21, n, round(polchebyshev(n-1, 2, (4+sqrt(2))/2)*polchebyshev(n-1, 2, (4-sqrt(2))/2)) ) \\ _G. C. Greubel_, Dec 24 2019
%o A161158 (Sage) [round(chebyshev_U(n,(4+sqrt(2))/2)*chebyshev_U(n,(4-sqrt(2))/2)) for n in (0..20)] # _G. C. Greubel_, Dec 24 2019
%o A161158 (GAP) a:=[1,14,161,1792];; for n in [5..20] do a[n]:=14*a[n-1]-34*a[n-2] +14*a[n-3] -a[n-4]; od; a; # _G. C. Greubel_, Dec 24 2019
%Y A161158 Cf. A001563, A003696, A100047.
%K A161158 nonn,easy
%O A161158 0,2
%A A161158 _R. J. Mathar_, Jun 03 2009