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 A224232 #52 Aug 28 2023 16:34:23
%S A224232 1,1,2,6,16,42,112,298,792,2106,5600,14890,39592,105274,279920,744298,
%T A224232 1979064,5262266,13992192,37204778,98926280,263041722,699419280,
%U A224232 1859732842,4944968408,13148508218,34961450528,92961346090,247181159144,657246565434,1747596982192,4646802848106,12355695809272,32853388431034,87356078367552,232276936784682
%N A224232 a(n) = n! if n <= 3, otherwise a(n) = 2*(a(n-1) + a(n-3)) + a(n-2).
%C A224232 Also the number of permutations that are sortable after two passes through a pop stack. (See the Pudwell-Smith link.) - _Lara Pudwell_, Jun 01 2017
%H A224232 Colin Barker, <a href="/A224232/b224232.txt">Table of n, a(n) for n = 0..1000</a>
%H A224232 G. Aleksandrowich et al., <a href="https://doi.org/10.1016/j.disc.2013.01.028">Permutations with forbidden patterns and polyominoes on a twisted cylinder of width 3</a>, Discrete Math., 313 (2013), 1078-1086.
%H A224232 Anders Claesson and Bjarki Ágúst Guðmundsson, <a href="https://arxiv.org/abs/1710.04978">Enumerating permutations sortable by k passes through a pop-stack</a>, arXiv:1710.04978 [math.CO], 2017.
%H A224232 Lara Pudwell and Rebecca Smith, <a href="http://faculty.valpo.edu/lpudwell/slides/AMS2017_pudwell.pdf">Sorting with Pop Stacks</a>, Special Session on Algebraic and Enumerative Combinatorics with Applications, AMS Central Section Spring Meeting, 2017.
%H A224232 Lara Pudwell and Rebecca Smith, <a href="https://arxiv.org/abs/1801.05005">Two-stack-sorting with pop stacks</a>, arXiv:1801.05005 [math.CO], 2018.
%H A224232 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,2).
%F A224232 G.f.: (x^3 + x^2 + x - 1) / (2*x^3 + x^2 + 2*x - 1). - _Colin Barker_, Jun 07 2015
%F A224232 a(n) = (b(n) + b(n-1))/2 for b(n) = A077996(n). - _Hanzhang Fang_, Aug 27 2022
%t A224232 CoefficientList[Series[(x^3 + x^2 + x - 1)/(2 x^3 + x^2 + 2 x - 1), {x, 0, 35}], x] (* _Michael De Vlieger_, Jun 01 2017 *)
%t A224232 LinearRecurrence[{2,1,2},{1,1,2,6},40] (* _Harvey P. Dale_, Aug 28 2023 *)
%o A224232 (PARI) Vec((x^3+x^2+x-1)/(2*x^3+x^2+2*x-1) + O(x^100)) \\ _Colin Barker_, Jun 07 2015
%Y A224232 Cf. A077996, A293774, A293775, A293776, A293784.
%K A224232 nonn,easy
%O A224232 0,3
%A A224232 _N. J. A. Sloane_, Apr 11 2013