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 A172193 #23 May 16 2025 13:25:05
%S A172193 1,37,83,139,205,281,367,463,569,685,811,947,1093,1249,1415,1591,1777,
%T A172193 1973,2179,2395,2621,2857,3103,3359,3625,3901,4187,4483,4789,5105,
%U A172193 5431,5767,6113,6469,6835,7211,7597,7993,8399,8815,9241,9677,10123,10579
%N A172193 a(n) = 5*n^2 + 31*n + 1.
%H A172193 Vincenzo Librandi, <a href="/A172193/b172193.txt">Table of n, a(n) for n = 0..1000</a>
%H A172193 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A172193 G.f.: (1+34*x-25*x^2)/(1-x)^3.
%F A172193 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Vincenzo Librandi_, Apr 07 2013
%F A172193 E.g.f.: (1 + 36*x + 5*x^2)*exp(x). - _G. C. Greubel_, Apr 28 2022
%t A172193 CoefficientList[Series[(1 +34x -25x^2)/(1-x)^3, {x, 0, 60}], x] (* _Vincenzo Librandi_, Apr 07 2013 *)
%t A172193 LinearRecurrence[{3,-3,1},{1,37,83},50] (* _Harvey P. Dale_, May 16 2025 *)
%o A172193 (Magma) [ 5*n^2+31*n+1: n in [0..50] ];
%o A172193 (PARI) a(n)=5*n^2+31*n+1 \\ _Charles R Greathouse IV_, Jun 17 2017
%o A172193 (SageMath) [((10*n+31)^2 -941)/20 for n in (0..50)] # _G. C. Greubel_, Apr 28 2022
%Y A172193 Cf. A172043 (5*n^2-n+1).
%K A172193 nonn,easy
%O A172193 0,2
%A A172193 _Vincenzo Librandi_, Jan 29 2010
%E A172193 Replaced definition with formula. - _N. J. A. Sloane_, Mar 03 2010