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 A270809 #18 Jul 18 2025 14:33:36
%S A270809 4,2,2,6,16,34,62,102,156,226,314,422,552,706,886,1094,1332,1602,1906,
%T A270809 2246,2624,3042,3502,4006,4556,5154,5802,6502,7256,8066,8934,9862,
%U A270809 10852,11906,13026,14214,15472,16802,18206,19686,21244,22882,24602,26406,28296,30274
%N A270809 a(n) = n^3/3 - 7*n/3 + 4.
%H A270809 M. Diepenbroek, M. Maus, A. Stoll, <a href="http://www.valpo.edu/mathematics-statistics/files/2014/09/Pudwell2015.pdf">Pattern Avoidance in Reverse Double Lists</a>, Preprint 2015. See Theorem 3.14.
%H A270809 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A270809 O.g.f.: (4 - 14*x + 18*x^2 - 6*x^3)/(1-x)^4. - _Vincenzo Librandi_, Apr 08 2016
%F A270809 E.g.f.: (12 - 6*x + 3*x^2 + x^3)*exp(x)/3. - _Bruno Berselli_, Apr 08 2016
%F A270809 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>3. - _Vincenzo Librandi_, Apr 08 2016
%F A270809 a(n) = 2*A105163(n) for n>0. - _Bruno Berselli_, Apr 08 2016
%t A270809 Table[n^3 / 3 - 7 n / 3 + 4, {n, 0, 50}] (* _Vincenzo Librandi_, Apr 08 2016 *)
%t A270809 LinearRecurrence[{4,-6,4,-1},{4,2,2,6},50] (* _Harvey P. Dale_, Jul 18 2025 *)
%o A270809 (Magma) [n^3/3-7*n/3+4: n in [0..50]]; // _Vincenzo Librandi_, Apr 08 2016
%o A270809 (PARI) vector(50, n, n--; n^3/3-7*n/3+4) \\ _Bruno Berselli_, Apr 08 2016
%o A270809 (PARI) x='x+O('x^99); Vec((4-14*x+18*x^2-6*x^3)/(1-x)^4) \\ _Altug Alkan_, Apr 08 2016
%o A270809 (Sage) [n^3/3-7*n/3+4 for n in [0..50]] # _Bruno Berselli_, Apr 08 2016
%Y A270809 Cf. A105163.
%K A270809 nonn,easy
%O A270809 0,1
%A A270809 _N. J. A. Sloane_, Apr 06 2016