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 A248163 #26 Jun 01 2025 16:37:40
%S A248163 1,34,1147,38692,1305205,44028742,1485230383,50101574344,
%T A248163 1690086454249,57012025275370,1923198081274339,64875626535849196,
%U A248163 2188462519487403613,73823845023749080078,2490314568132082090135,84006280711277049343888,2833800713070230938880977,95593167717986358477858226
%N A248163 Chebyshev's S polynomials (A049310) evaluated at 34/3 and multiplied by powers of 3 (A000244).
%C A248163 This sequence appears in the solution for the curvature sequence of the touching circle and chord example given in A249457. See also the pair A249862(n) and a(n-1), with a(-1) = 0, for which details are given in A249862.
%H A248163 G. C. Greubel, <a href="/A248163/b248163.txt">Table of n, a(n) for n = 0..650</a>
%H A248163 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (34,-9).
%F A248163 a(n) = 3^n*S(n, 34/3) with Chebyshev's S polynomial (for S see the coefficient triangle A049310).
%F A248163 O.g.f.: 1/(1 - 34*x + 9*x^2).
%F A248163 a(n) = 34*a(n-1) - 9*a(n-2), a(-1) = 0, a(0) = 1 .
%F A248163 E.g.f.: exp(17*x)*(140*cosh(2*sqrt(70)*x) + 17*sqrt(70)*sinh(2*sqrt(70)*x))/140. - _Stefano Spezia_, Mar 24 2023
%t A248163 CoefficientList[Series[1/(1-34 x +(3 x)^2), {x,0,40}], x] (* _Vincenzo Librandi_, Nov 08 2014 *)
%t A248163 Table[3^n*ChebyshevU[n,17/3], {n,0,40}] (* _G. C. Greubel_, May 31 2025 *)
%o A248163 (Magma) I:=[1, 34]; [n le 2 select I[n] else 34*Self(n-1) - 9*Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, Nov 08 2014
%o A248163 (SageMath)
%o A248163 def A248163(n): return 3^n*chebyshev_U(n,17/3)
%o A248163 print([A248163(n) for n in range(41)]) # _G. C. Greubel_, May 31 2025
%o A248163 (PARI) a(n) = 3^n*polchebyshev(n, 2, 17/3); \\ _Michel Marcus_, May 31 2025
%Y A248163 Cf. A000244, A049310, A249457, A249862.
%K A248163 nonn,easy
%O A248163 0,2
%A A248163 _Wolfdieter Lang_, Nov 07 2014
%E A248163 a(16)-a(17) from _Stefano Spezia_, Mar 24 2023