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A000802
Maximal number of states in the minimal deterministic finite automaton accepting a language over a binary alphabet consisting of some words of length n.
1
1, 2, 4, 7, 11, 19, 34, 50, 82, 146, 274, 529, 785, 1297, 2321, 4369, 8465, 16657, 33041, 65809, 131344, 196880, 327952, 590096, 1114384, 2162960, 4260112, 8454416, 16843024, 33620240, 67174672, 134283536, 268501264, 536936720, 1073807632, 2147549456, 4295033104
OFFSET
0,2
LINKS
J.-M. Champarnaud and J.-E. Pin,A maxmin problem on finite automata,Discrete Appl. Math. 23 (1989), no. 1, 91-96.
FORMULA
a(n) = Sum_{k=0..n} min(2^k,2^(2^(n-k))-1). -Sean A. Irvine,Jun 24 2011
MAPLE
a:= n-> add((t-> `if`(t>k, 2^k, 2^t-1))(2^(n-k)), k=0..n):
seq(a(n), n=0..36); #Alois P. Heinz,Apr 13 2022
PROG
(PARI) a(n) = sum(k=0, n, min(2^k, 2^(2^(n-k))-1)) \\ (works while n<29)Michel Marcus,May 25 2013
KEYWORD
nonn
EXTENSIONS
a(34)-a(36) fromSean A. Irvine,Jun 23 2011
STATUS
approved