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 A386486 #17 Sep 03 2025 09:16:00
%S A386486 1,3,12,29,54,87,128,177,234,299,372,453,542,639,744,857,978,1107,
%T A386486 1244,1389,1542,1703,1872,2049,2234,2427,2628,2837,3054,3279,3512,
%U A386486 3753,4002,4259,4524,4797,5078,5367,5664,5969,6282,6603,6932,7269,7614,7967,8328,8697,9074,9459,9852,10253,10662,11079,11504,11937,12378
%N A386486 a(0) = 1; thereafter a(n) = 4*n^2 - 3*n + 2.
%C A386486 Differs from A001107, A054552, and A343560 only by a small constant, but has its own entry because of an important geometric application (which will be added soon).
%H A386486 Paolo Xausa, <a href="/A386486/b386486.txt">Table of n, a(n) for n = 0..10000</a>
%H A386486 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A386486 From _Elmo R. Oliveira_, Sep 02 2025: (Start)
%F A386486 G.f.: (1 + 6*x^2 + x^3)/(1 - x)^3.
%F A386486 E.g.f.: exp(x)*(2 + x + 4*x^2) - 1.
%F A386486 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 3. (End)
%t A386486 A386486[n_] := If[n == 0, 1, (4*n - 3)*n + 2]; Array[A386486, 100, 0] (* or *)
%t A386486 LinearRecurrence[{3, -3, 1}, {1, 3, 12, 29}, 100] (* _Paolo Xausa_, Aug 27 2025 *)
%Y A386486 Cf. A001107, A054552, A343560.
%K A386486 nonn,easy,new
%O A386486 0,2
%A A386486 _N. J. A. Sloane_, Aug 27 2025