A307154 Decimal expansion of the fraction of occupied places on an infinite lattice cover with 3-length segments.

8, 2, 3, 6, 5, 2, 9, 6, 3, 1, 7, 7, 3, 3, 8, 3, 3, 6, 9, 0, 0, 6, 7, 1, 8, 7, 7, 8, 1, 1, 6, 4, 7, 8, 8, 7, 2, 1, 3, 9, 2, 3, 6, 6, 2, 0, 5, 3, 9, 2, 9, 8, 6, 8, 0, 9, 1, 4, 3, 7, 2, 3, 5, 0, 0, 7, 1, 8, 2, 2, 0, 1, 8, 0, 9, 8, 1, 2, 0, 0, 7, 9, 0, 9, 0, 5, 5, 8, 9, 2, 6, 4, 8, 7, 4, 0, 3, 0, 3, 3, 7, 1, 9, 6, 3, 8, 5, 4, 5, 9, 2, 8, 8, 9, 7, 9, 3, 3, 4, 2, 4, 8, 8, 7, 7, 2, 1, 2, 7, 1, 9, 6

Offset

0,1

Comments

Solution of the discrete parking problem when infinite lattice randomly filled with 3-length segments.

Solution of the discrete parking problem when infinite lattice randomly filled with 2-length segments is equal to 1-1/e^2 (see A219863).

Also, the limit of a(n) = (3 + 2*(n-3)*a(n-3) + (n-1)*(n-3)*a(n-1))/(n*(n-2)); a(0) = 0; a(1) = 0; a(2) = 0 as n tends to infinity.

If the length of the segments that randomly cover infinite lattice tends to infinity, then the fraction of occupied places is equal to Rényi's parking constant (see A050996).

Links

Table of n, a(n) for n=0..131.

D. G. Radcliffe, Fat men sitting at a bar

Philipp O. Tsvetkov, Stoichiometry of irreversible ligand binding to a one-dimensional lattice, Scientific Reports, Springer Nature (2020) Vol. 10, Article number: 21308.

Eric Weisstein's World of Mathematics, Dawson's Integral

Formula

Equals 3*(Dawson(2) - Dawson(1)/e^3).

Equals 3*sqrt(Pi)*(erfi(2) - erfi(1)) / (2*exp(4)).

Example

0.8236529631773383369006718778116478872139236620539298680914372350071822...

Maple

evalf(3*sqrt(Pi)*(erfi(2)-erfi(1))/(2*exp(4)), 120) # Vaclav Kotesovec, Mar 28 2019

Mathematica

N[-((3 DawsonF[1])/E^3) + 3 DawsonF[2], 200] // RealDigits

Prog

(PARI) -imag(3*sqrt(Pi)*(erfc(2*I) - erfc(1*I)) / (2*exp(4))) \\ Michel Marcus, May 10 2019

Crossrefs

Cf. A050996, A087654, A099288, A219863, A307131, A307132.

Sequence in context: A140244 A160105 A167162 * A298920 A254268 A247684

Adjacent sequences: A307151 A307152 A307153 * A307155 A307156 A307157

Keyword

nonn,cons

Author

Philipp O. Tsvetkov, Mar 27 2019

Status

approved