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 A382570 #19 Apr 01 2025 20:18:55
%S A382570 1,1,2,5,14,41,121,355,1037,3025,8824,25746,75130,219246,639805,
%T A382570 1867066,5448412,15899370,46397015,135394275,395103258,1152977744,
%U A382570 3364582879,9818418346,28651794889,83610752932,243990229487,712004497223,2077748790043,6063220178075
%N A382570 a(n) is the number of shallow permutations of length n that avoid 231.
%C A382570 A shallow permutation is a permutation that satisfies the lower bound of the Diaconis-Graham inequality (i.e., so that the total displacement is equal to the sum of the length and reflection length).
%H A382570 Michael De Vlieger, <a href="/A382570/b382570.txt">Table of n, a(n) for n = 0..2151</a>
%H A382570 Kassie Archer, Aaron Geary, and Robert P. Laudone, <a href="https://arxiv.org/abs/2412.11999">Pattern-avoiding shallow permutations</a>, arXiV:2412.11999 [math.CO], 2024
%H A382570 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4,2,1,1).
%F A382570 G.f: (1-3*x+2*x^2-x^3-x^4-x^5)/(1-4*x+4*x^2-2*x^3-x^4-x^5).
%t A382570 CoefficientList[Series[(1 - 3*x + 2*x^2 - x^3 - x^4 - x^5)/(1 - 4*x + 4*x^2 - 2*x^3 -x^4 - x^5), {x, 0, 29}], x] (* _Michael De Vlieger_, Apr 01 2025 *)
%Y A382570 Cf. A062869, A301897.
%K A382570 nonn,easy
%O A382570 0,3
%A A382570 _Kassie Archer_, Mar 31 2025