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A102866
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Number of finite languages over a binary alphabet (set of binary words of total length n).
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2
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1, 2, 5, 16, 42, 116, 310, 816, 2121, 5466, 13937, 35248, 88494, 220644, 546778, 1347344, 3302780, 8057344, 19568892, 47329264, 114025786, 273709732, 654765342, 1561257968, 3711373005, 8797021714, 20794198581, 49024480880
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Analogous to A034899 (which also enumerates multisets of words)
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REFERENCES
| Stefan Gerhold, Counting finite languages by total word length, INTEGERS 11 (2011), #A44; http://www.emis.de/journals/INTEGERS/papers/l44/l44.pdf.
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LINKS
| Alois P. Heinz, Table of n, a(n) for n = 0..900
P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009; see page 64
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FORMULA
| GF: exp(Sum((-1)^(j-1)/j*(2*z^j)/(1-2*z^j), j=1..infinity)):
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EXAMPLE
| a(2)=5 because the sets are {a,b}, {aa}, {ab}, {ba}, {bb};
a(3)=16 because the sets are {a,aa}, {a,ab}, {a,ba}, {a,bb}, {b,aa}, {b,ab}, {b,ba}, {b,bb}, {aaa}, {aab}, {aba}, {abb}, {baa}, {bab}, {bba}, {bbb}
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MAPLE
| series(exp(add((-1)^(j-1)/j*(2*z^j)/(1-2*z^j), j=1..40)), z, 40);
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CROSSREFS
| Cf. A034899.
Sequence in context: A188947 A076958 A163825 * A148368 A148369 A148370
Adjacent sequences: A102863 A102864 A102865 * A102867 A102868 A102869
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KEYWORD
| nonn
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AUTHOR
| Philippe Flajolet (Philippe.Flajolet(AT)inria.fr), Mar 01 2005
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