A209900 Floor of the expected number of occupied cells in a random placement of 2n balls into n cells.

1, 1, 2, 3, 4, 5, 6, 7, 7, 8, 9, 10, 11, 12, 13, 13, 14, 15, 16, 17, 18, 19, 20, 20, 21, 22, 23, 24, 25, 26, 26, 27, 28, 29, 30, 31, 32, 32, 33, 34, 35, 36, 37, 38, 39, 39, 40, 41, 42, 43, 44, 45, 45, 46, 47, 48, 49, 50, 51, 52, 52, 53, 54, 55, 56, 57, 58, 58

Offset

1,3

Comments

Also floor of expected number of distinct symbols in sequences on n symbols of length 2n.

Links

Table of n, a(n) for n=1..68.

Formula

a(n) = floor(n*(1-(1-1/n)^(2*n))).

Example

For n=2, with symbols 0 and 1, the 2^4 sequences on 2 symbols of length 4 can be represented by 0000, 0001, 0010, 0011, 0100, 0101, 0110, 0111, 1000, 1001, 1010, 1011, 1100, 1101, 1110, and 1111. We have 2 sequences with a unique symbol, and 14 sequences with 2 symbols, so a(2) = floor((14*2+2)/16) = floor(15/8) = 1.

Mathematica

Table[Floor[n*(1 - (1 - 1/n)^(2 n))], {n, 100}] (* T. D. Noe, Mar 15 2012 *)

Crossrefs

Cf. A209899.

Sequence in context: A157466 A194260 A227394 * A097043 A245336 A356964

Adjacent sequences: A209897 A209898 A209899 * A209901 A209902 A209903

Keyword

nonn

Author

Washington Bomfim, Mar 14 2012

Status

approved