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 A116735 #29 Sep 08 2022 08:45:24
%S A116735 1,2,5,12,23,38,57,80,107,138,173,212,255,302,353,408,467,530,597,668,
%T A116735 743,822,905,992,1083,1178,1277,1380,1487,1598,1713,1832,1955,2082,
%U A116735 2213,2348,2487,2630,2777,2928,3083,3242,3405,3572,3743,3918,4097,4280,4467
%N A116735 Number of permutations of length n which avoid the patterns 231, 1234, 4312; or avoid the patterns 312, 1234, 1432, etc.
%C A116735 a(n) is the number of permutations pi of length n such that pi and pi^2 both avoid 132 and 3421. - _Colin Defant_, Jul 24 2019
%H A116735 Vincenzo Librandi, <a href="/A116735/b116735.txt">Table of n, a(n) for n = 1..1000</a>
%H A116735 Miklos Bona and Rebecca Smith, <a href="https://arxiv.org/abs/1901.00026">Pattern Avoidance in Permutations and Their Squares</a>, arXiv:1901.00026 [math.CO], 2019.
%H A116735 Amanda Burcroff and Colin Defant, <a href="https://arxiv.org/abs/1907.09451">Pattern-Avoiding Permutation Powers</a>, arXiv:1907.09451 [math.CO], 2019.
%H A116735 Lara Pudwell, <a href="http://faculty.valpo.edu/lpudwell/maple/webbook/bookmain.html">Systematic Studies in Pattern Avoidance</a>, 2005.
%H A116735 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3, -3, 1).
%F A116735 G.f.: x*(1 - x + 2*x^2 + 2*x^3)/(1-x)^3.
%F A116735 For n >= 2, a(n) = 2*n^2 - 7*n + 8. - _Franklin T. Adams-Watters_, Sep 16 2006
%F A116735 a(n) = A096376(n-2), n > 1. - _R. J. Mathar_, Aug 10 2008
%F A116735 E.g.f.: -8 - 2*x + (8 - 5*x + 2*x^2)*exp(x). - _G. C. Greubel_, Aug 10 2019
%p A116735 A116735:=n->`if`(n=1, 1, 2*n^2-7*n+8); seq(A116735(n), n=1..50); # _G. C. Greubel_, Aug 10 2019
%t A116735 Join[{1}, LinearRecurrence[{3, -3, 1}, {2, 5, 12}, 80]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 18 2012 *)
%o A116735 (PARI) vector(50, n, if(n<2, n, 2*n^2-7*n+8)) \\ _G. C. Greubel_, Aug 10 2019
%o A116735 (Magma) [n lt 2 select n else 2*n^2-7*n+8: n in [1..50]]; // _G. C. Greubel_, Aug 10 2019
%o A116735 (Sage) [1]+[2*n^2-7*n+8 for n in (2..50)] # _G. C. Greubel_, Aug 10 2019
%o A116735 (GAP) Concatenation([1], List([2..50], n-> 2*n^2-7*n+8)); # _G. C. Greubel_, Aug 10 2019
%K A116735 nonn,easy
%O A116735 1,2
%A A116735 _Lara Pudwell_, Feb 26 2006