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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)
21
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)
OFFSET

1,4

COMMENTS

a(n) <= A002955(n) [From Max Alekseyev, Sep 23 2009]

REFERENCES

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).

LINKS

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

EXAMPLE

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

CROSSREFS

Cf. A003018, A003019, A145545, A145546, A145547, A145548, A145549, A145550, A000081.

Sequence in context: A190162 A157904 A182901 * A072925 A002955 A202844

Adjacent sequences:  A002842 A002843 A002844 * A002846 A002847 A002848

KEYWORD

nonn,nice,more

AUTHOR

N. J. A. Sloane.

EXTENSIONS

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

STATUS

approved

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Last modified September 17 23:53 EDT 2014. Contains 246886 sequences.