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A002845
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Number of distinct values taken by 2^2^...^2 (with n 2's and parentheses inserted in all possible ways).
(Formerly M1139 N0435)
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22
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1, 1, 1, 2, 4, 8, 17, 36, 78, 171, 379, 851, 1928, 4396, 10087, 23273, 53948, 125608, 293543, 688366, 1619087, 3818818, 9029719, 21400706, 50828664, 120963298, 288405081
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OFFSET
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1,4
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COMMENTS
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a(n) <= A002955(n). - Max Alekseyev, Sep 23 2009
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REFERENCES
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F. Goebel and R. P. Nederpelt, The number of numerical outcomes of iterated powers, Amer. Math. Monthly, 80 (1971), 1097-1103.
R. K. Guy and J. L. Selfridge, The nesting and roosting habits of the laddered parenthesis. Amer. Math. Monthly 80 (1973), 868-876.
J. Q. Longyear, personal communication.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Table of n, a(n) for n=1..27.
Jon E. Schoenfield, The 851 values for n=12
R. K. Guy and J. L. Selfridge, The nesting and roosting habits of the laddered parenthesis (annotated cached copy)
Index entries for sequences related to parenthesizing
MathOverflow discussion of related questions
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EXAMPLE
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When n=3, 2^(2^2) = (2^2)^2 = 16, so a(3) = 1.
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CROSSREFS
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Cf. A003018, A003019, A145545, A145546, A145547, A145548, A145549, A145550, A000081.
Sequence in context: A251691 A157904 A182901 * A072925 A002955 A202844
Adjacent sequences: A002842 A002843 A002844 * A002846 A002847 A002848
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KEYWORD
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nonn,nice,more
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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a(12)-a(13) corrected and a(14)-a(27) added by Jon E. Schoenfield, Oct 11 2008
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STATUS
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approved
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