login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A307132
Denominator of the expected fraction of occupied places on n-length lattice randomly filled with 2-length segments.
3
1, 3, 6, 5, 45, 63, 420, 405, 14175, 17325, 187110, 552825, 14189175, 49116375, 729729000, 723647925, 8881133625, 109185701625, 2062396586250, 10257709336875, 428772250281375, 2348038513445625, 53791427762572500, 160789593855515625, 16025362854266390625
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).
FORMULA
Denominator 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}] // Denominator
CROSSREFS
Cf. A219863, A231580, A307131 (numerators).
Sequence in context: A115389 A303564 A121867 * A300673 A335633 A009193
KEYWORD
nonn,frac
AUTHOR
Philipp O. Tsvetkov, Mar 26 2019
STATUS
approved