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 A179257 #18 May 19 2024 13:04:50
%S A179257 1,1,2,5,13,32,72,148,281,499,838,1343,2069,3082,4460,6294,8689,11765,
%T A179257 15658,20521,26525,33860,42736,53384,66057,81031,98606,119107,142885,
%U A179257 170318,201812,237802,278753,325161,377554,436493,502573,576424,658712,750140,851449
%N A179257 Number of permutations of length n which avoid the patterns 321 and 1324.
%H A179257 M. D. Atkinson, <a href="https://doi.org/10.1016/S0012-365X(98)00162-9">Restricted permutations</a>, Discrete Math., 195 (1999), 27-38.
%H A179257 Christian Bean, Bjarki Gudmundsson, Henning Ulfarsson, <a href="https://arxiv.org/abs/1705.04109">Automatic discovery of structural rules of permutation classes</a>, arXiv:1705.04109 [math.CO], 2017.
%H A179257 J. West, <a href="https://doi.org/10.1016/S0012-365X(96)83023-8">Generating trees and forbidden subsequences</a>, Discrete Math., 157 (1996), 363-374.
%H A179257 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F A179257 a(n) = 1+binomial(n,2)+binomial(n+2,5).
%F A179257 G.f.: 1-x*(x^5-4*x^4+7*x^3-8*x^2+4*x-1)/(x-1)^6. - _Colin Barker_, Aug 02 2012
%F A179257 a(n) = 1+A027658(n-2). - _R. J. Mathar_, Aug 19 2022
%e A179257 There are 13 permutations of length 4 which avoid these two patterns, so a(4)=13.
%t A179257 LinearRecurrence[{6,-15,20,-15,6,-1},{1,1,2,5,13,32},50] (* _Harvey P. Dale_, May 19 2024 *)
%Y A179257 Cf. A116699, A116701, A116702, A088921, A005183, A116703, A001519.
%K A179257 nonn,easy
%O A179257 0,3
%A A179257 _Vincent Vatter_, Jul 05 2010
%E A179257 a(0)=1 prepended by _Alois P. Heinz_, Jul 05 2018