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 A317793 #42 Sep 08 2022 08:46:22
%S A317793 1,15,22,177,406,2445,7162,36177,121486,554325,2009602,8656377,
%T A317793 32761366,136617405,529712842,2169039777,8525430046,34553579685,
%U A317793 136858084882,551499730377,2193794127526,8811785649165,35137304693722,140878711512177,562526325893806
%N A317793 a(n) = (4^n + (-3)^n + 2^n + (-1)^n)/2.
%C A317793 This sequence is an extension of A014551; the sequences A014551(n) = 2^n + (-1)^n, a(n) = 4^n + (-3)^n + 2^n + (-1)^n and b(n) = 6^n + (-5)^n + 4^n + (-3)^n + 2^n + (-1)^n, ... can be considered to be of the same type.
%C A317793 For k>0, a(4k-2)/5, a(2k)/3 and a(2k+1)/2 are integers.
%H A317793 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,13,-14,-24).
%F A317793 a(n) = (4^n + (-3)^n + 2^n + (-1)^n)/2 for n > 0.
%F A317793 From _Colin Barker_, Aug 07 2018: (Start)
%F A317793 G.f.: x*(1 + 13*x - 21*x^2 - 48*x^3) / ((1 + x)*(1 - 2*x)*(1 + 3*x)*(1 - 4*x)).
%F A317793 a(n) = 2*a(n-1) + 13*a(n-2) - 14*a(n-3) - 24*a(n-4) for n>4.
%F A317793 (End)
%F A317793 E.g.f.: (cosh(3*x/2) + cosh(7*x/2))*(cosh(x/2) + sinh(x/2)) - 2. - _Stefano Spezia_, Mar 20 2022
%t A317793 CoefficientList[ Series[(-48x^3 - 21x^2 + 13x + 1)/(24x^4 + 14x^3 - 13x^2 - 2x + 1), {x, 0, 25}], x] (* or *)LinearRecurrence[{2, 13, -14, -24}, {1, 15, 22, 177}, 26] (* _Robert G. Wilson v_, Aug 07 2018 *)
%o A317793 (PARI) Vec(x*(1 + 13*x - 21*x^2 - 48*x^3) / ((1 + x)*(1 - 2*x)*(1 + 3*x)*(1 - 4*x)) + O(x^40)) \\ _Colin Barker_, Aug 07 2018
%o A317793 (Magma) [(4^n+(-3)^n+2^n+(-1)^n)/2: n in [1..30]]; // _Vincenzo Librandi_, Aug 08 2018
%Y A317793 Cf. A014551, A087451.
%K A317793 nonn,easy
%O A317793 1,2
%A A317793 _Jinyuan Wang_, Aug 07 2018
%E A317793 More terms from _Colin Barker_, Aug 07 2018