OFFSET
1,3
COMMENTS
Also floor of expected number of distinct symbols in sequences on n symbols of length 2n.
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
KEYWORD
nonn
AUTHOR
Washington Bomfim, Mar 14 2012
STATUS
approved