A307131 Numerator of the expected fraction of occupied places on n-length lattice randomly filled with 2-length segments.

1, 2, 5, 4, 37, 52, 349, 338, 11873, 14554, 157567, 466498, 11994551, 41582906, 618626159, 614191052, 7545655031, 92853583996, 1755370057489, 8737266957604, 365468962351379, 2002633668589496, 45904893141293831

Offset

1,2

Comments

The limit of expected fraction of occupied places on n-length lattice randomly filled with 2-length segments at n tends to infinity is equal to 1-1/e^2 (see A219863).

Links

Table of n, a(n) for n=1..23.

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

Formula

Numerator of f(n), where f(0)=0; f(1)=0 and f(n) = (2 + 2(n-2)f(n-2) + (n-1)(n-2)f(n-1))/(n(n-1)) for n>1.

Example

0, 1, 2/3, 5/6, 4/5, 37/45, 52/63, 349/420, 338/405, 11873/14175, ...

Mathematica

RecurrenceTable[{f[n] == (2 + 2 (n - 2) f[n - 2] + (n - 1) (n - 2) f[n - 1])/(n (n - 1)), f[0] == 0, f[1] == 0}, f, {n, 2, 100}] // Numerator

Crossrefs

Cf. A219863, A231580, A307132 (denominators).

Sequence in context: A319770 A229789 A357240 * A210419 A206484 A061083

Adjacent sequences: A307128 A307129 A307130 * A307132 A307133 A307134

Keyword

nonn,frac

Author

Philipp O. Tsvetkov, Mar 26 2019

Status

approved