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A003018
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Number of distinct values taken by 3^3^...^3 (with n 3's and parentheses inserted in all possible ways).
(Formerly M1178)
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26
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1, 1, 2, 4, 9, 20, 47, 111, 270, 664, 1659, 4184, 10662, 27367, 70747, 183925, 480656, 1261630, 3324772, 8792592, 23327249, 62067785, 165586565
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OFFSET
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1,3
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COMMENTS
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The g.f. (-1+z+6*z**2-3*z**3-8*z**4+3*z**5)/(-1+2*z+6*z**2-9*z**3-10*z**4+9*z**5) conjectured by Simon Plouffe in his 1992 dissertation is wrong.
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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.
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..23.
R. K. Guy and J. L. Selfridge, The nesting and roosting habits of the laddered parenthesis (annotated cached copy)
_Simon Plouffe_, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
_Simon Plouffe_, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Index entries for sequences related to parenthesizing
MathOverflow discussion of related questions
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CROSSREFS
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Cf. A002845, A003019, A145545, A145546, A145547, A145548, A145549, A145550, A000081.
Sequence in context: A130802 A022543 A036618 * A196244 A035084 A213905
Adjacent sequences: A003015 A003016 A003017 * A003019 A003020 A003021
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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(23) from Jon Schoenfield (jonscho(AT)hiwaay.net), Oct 11 2008
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STATUS
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approved
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