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 A269112 #47 Oct 04 2024 16:36:28
%S A269112 3,5,11,21,33,47,65,87,111,137,167,201,237,275,317,363,411,461,515,
%T A269112 573,633,695,761,831,903,977,1055,1137,1221,1307,1397,1491,1587,1685,
%U A269112 1787,1893,2001,2111,2225,2343,2463,2585,2711,2841,2973,3107,3245,3387,3531,3677,3827
%N A269112 a(n) = (3*(n-1)*n + (-1)^((n-1)*n/2) + 5)/2.
%H A269112 Bruno Berselli, <a href="/A269112/b269112.txt">Table of n, a(n) for n = 1..1000</a>
%H A269112 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-4,4,-3,1).
%F A269112 G.f.: x*(3 - 4*x + 8*x^2 - 4*x^3 + 3*x^4)/((1 + x^2)*(1 - x)^3).
%F A269112 a(n) = (3*n^2 - 3*n + cos(n*Pi/2) + sin(n*Pi/2) + 5)/2.
%F A269112 a(n) = 3*(n-1)^2 - 3*(n-1) - a(n-2) + 8 for n>2.
%F A269112 a(n) = 3*a(n-1) - 4*a(n-2) + 4*a(n-3) - 3*a(n-4) + a(n-5) for n>5. - _Colin Barker_, Feb 22 2016
%F A269112 a(n) = A047270(A000124(n-1)). - _Bruno Berselli_, Feb 23 2016
%t A269112 Table[(3 (n - 1) n + (-1)^((n - 1) n/2) + 5)/2, {n, 100}]
%t A269112 LinearRecurrence[{3, -4, 4, -3, 1}, {3, 5, 11, 21, 33}, 100]
%t A269112 CoefficientList[Series[(3-4*x+8*x^2-4*x^3+3*x^4)/((1+x^2)*(1-x)^3), {x, 0, 100}], x]
%o A269112 (PARI) Vec((3-4*x+8*x^2-4*x^3+3*x^4)/((1+x^2)*(1-x)^3) + O(x^60)) \\ _Michel Marcus_, Feb 22 2016
%o A269112 (Magma) I:=[3,5]; [n le 2 select I[n] else 3*(n-1)^2-3*(n-1)- Self(n-2)+8: n in [1..50]]; // _Vincenzo Librandi_, Feb 22 2016
%o A269112 (Sage) [(3*(n-1)*n+(-1)^((n-1)*n/2)+5)/2 for n in (1..50)] # _Bruno Berselli_, Feb 23 2016
%Y A269112 Cf. A005408, A047270.
%K A269112 nonn,easy
%O A269112 1,1
%A A269112 _Mikk Heidemaa_, Feb 19 2016
%E A269112 Edited by _Bruno Berselli_, Feb 23 2016