

A003018


Number of distinct values taken by 3^3^...^3 (with n 3's and parentheses inserted in all possible ways).
(Formerly M1178)


31



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

1,3


REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

Table of n, a(n) for n=1..23.
F. Goebel and R. P. Nederpelt, The number of numerical outcomes of iterated powers, Amer. Math. Monthly, 80 (1971), 10971103.
R. K. Guy and J. L. Selfridge, The nesting and roosting habits of the laddered parenthesis, Amer. Math. Monthly 80 (8) (1973), 868876.
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


CROSSREFS

Cf. A002845, A003019, A145545, A145546, A145547, A145548, A145549, A145550, A000081.
Sequence in context: A307557 A036618 A349014 * A196244 A035084 A213905
Adjacent sequences: A003015 A003016 A003017 * A003019 A003020 A003021


KEYWORD

nonn,nice,more


AUTHOR

N. J. A. Sloane


EXTENSIONS

a(12)a(23) from Jon E. Schoenfield, Oct 11 2008


STATUS

approved



