The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A210114 Floor of the expected value of number of trials until exactly three cells are empty in a random distribution of n balls in n cells. 5
 64, 10, 4, 2, 2, 2, 2, 3, 5, 7, 11, 18, 31, 55, 100, 185, 348, 670, 1311, 2606, 5254, 10734, 22196, 46407, 98023, 209009, 449580, 974963, 2130442, 4688533, 10387113, 23156162, 51926745, 117090391, 265413053 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,1 COMMENTS Also floor of the expected value of number of trials until we have n-3 distinct symbols in a random sequence on n symbols of length n. A055775 corresponds to zero cells empty. REFERENCES W. Feller, An Introduction to Probability Theory and its Applications, 2nd ed, Wiley, New York, 1965, (2.4) p. 92. (Occupancy problems) LINKS Washington Bomfim, Table of n, a(n) for n = 4..100 FORMULA With m = 3, a(n) = floor(n^n/(binomial(n,m)*_Sum{v=0..n-m-1}((-1)^v*binomial(n-m,v)*(n-m-v)^n))) EXAMPLE For n=4, there are 4^4 = 256 sequences on 4 symbols of length 4. Only 4 sequences have a unique symbol, so a(4) = floor(256/4) = 64. CROSSREFS Cf. A055775, A209899, A209900, A210112, A210113, A210115, A210116. Sequence in context: A288923 A123964 A298923 * A236179 A226044 A065790 Adjacent sequences:  A210111 A210112 A210113 * A210115 A210116 A210117 KEYWORD nonn AUTHOR Washington Bomfim, Mar 18 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 24 11:38 EDT 2020. Contains 337318 sequences. (Running on oeis4.)