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A002845 Number of distinct values taken by 2^2^...^2 (with n 2's and parentheses inserted in all possible ways).
(Formerly M1139 N0435)
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 (list; graph; refs; listen; history; text; internal format)



a(n) <= A002955(n). - Max Alekseyev, Sep 23 2009


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).


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


When n=3, 2^(2^2) = (2^2)^2 = 16, so a(3) = 1.


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




N. J. A. Sloane


a(12)-a(13) corrected and a(14)-a(27) added by Jon E. Schoenfield, Oct 11 2008



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Last modified August 29 10:37 EDT 2015. Contains 261188 sequences.