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
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
KEYWORD
nonn,frac
AUTHOR
Philipp O. Tsvetkov, Mar 26 2019
STATUS
approved