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 A307184 #23 Mar 24 2021 22:59:09
%S A307184 8,0,3,8,9,3,4,7,9,9,1,5,3,7,6,9,7,2,6,6,6,2,9,7,4,1,9,5,0,3,2,1,3,4,
%T A307184 2,0,5,4,6,8,7,9,1,6,4,8,5,7,7,0,8,3,5,9,2,3,9,7,2,9,9,3,2,8,0,7,0,9,
%U A307184 4,5,6,0,9,5,0,7,6,0,3,6,1,5
%N A307184 Decimal expansion of the fraction of occupied places on an infinite lattice cover with 4-length segments.
%C A307184 The solution of the discrete parking problem when infinite lattice randomly filled with L-length segments at L=4.
%C A307184 At L=3 it is equal to 3*(Dawson(2) - Dawson(1)/e^3) (see A307154).
%C A307184 At L=2 it is equal to 1-1/e^2 (see A219863).
%C A307184 The general solution of the discrete parking problem when infinite lattice randomly filled with L-length segments is equal to L*e(-2H(L-1))*Integral_{x=0..1} e^(2*(t + t^2/2 + t^3/3 + ... + t^(L-1)/(L-1))) dx, where H(L) is harmonic number.
%C A307184 Also, the limit of the following recurrence as n tends to infinity: a(n) = (4 + 2(n-4)*a(n-4) + (n-1)*(n-4)*a(n-1))/(n*(n-3)); a(0) = 0; a(1) = 0; a(2) = 0; a(3) = 0.
%C A307184 If L tends to infinity, then the fraction of occupied places is equal to Rényi's parking constant (see A050996).
%H A307184 D. G. Radcliffe, <a href="https://mathblag.files.wordpress.com/2012/12/fatmen.pdf">Fat men sitting at a bar</a>
%H A307184 Philipp O. Tsvetkov, <a href="https://doi.org/10.1038/s41598-020-77896-0">Stoichiometry of irreversible ligand binding to a one-dimensional lattice</a>, Scientific Reports, Springer Nature (2020) Vol. 10, Article number: 21308.
%F A307184 4*Integral_{x=0..1} e^(2*(t + t^2/2 + t^3/3)) dx / e^(11/3).
%e A307184 0.80389347991537697266629741950321342054687916485770835923972993280709456095...
%p A307184 evalf(Integrate(4*exp(2*(t + t^2/2 + t^3/3) - 11/3), t= 0..1), 120); # _Vaclav Kotesovec_, Mar 28 2019
%t A307184 RealDigits[ N[(4*Integrate[E^(2*(t + t^2/2 + t^3/3)), {t, 0, 1}])/E^(11/3), 200]][[1]]
%o A307184 (PARI) intnum(t=0, 1, 4*exp(2*(t + t^2/2 + t^3/3) - 11/3)) \\ _Michel Marcus_, May 10 2019
%Y A307184 Cf. A219863, A050996, A307132, A307131, A307154.
%K A307184 nonn,cons
%O A307184 0,1
%A A307184 _Philipp O. Tsvetkov_, Mar 28 2019