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

Author

Philipp O. Tsvetkov, Mar 26 2019

Keywords

• nonn
• frac

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).

Examples

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

Links

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

Crossrefs

Cf. A219863, A231580, A307132 (denominators).

Programs

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

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.