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A082499
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Take a string of n x's and insert n-1 ^'s and n-1 pairs of parentheses in all possible legal ways. Sequence gives number of distinct values when x = sqrt(2).
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5
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1, 1, 2, 4, 8, 17, 38, 88, 206, 497, 1212
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| For n=9, largest value is x^(x^(x^(x^(x^6)))) and results from the 132-th tree {0,{0,{0,{{{{{{0,0},0},0},0},0},0}}}} or {1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0}.
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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.
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LINKS
| R. K. Guy and J. L. Selfridge, The nesting and roosting habits of the laddered parenthesis (annotated cached copy)
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EXAMPLE
| For n = 4 there are 5 functions: f1(x) = ((x^x)^x)^x; f2(x) = (x^(x^x))^x; f3(x) = x^((x^x)^x); f4(x) = x^(x^(x^x)); f5(x) = (x^x)^(x^x); but only 4 different values when x = sqrt(2).
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CROSSREFS
| Cf. A003019, A000081, A002845, A003018, A082543.
Sequence in context: A112482 A193050 A107597 * A100131 A119685 A025276
Adjacent sequences: A082496 A082497 A082498 * A082500 A082501 A082502
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KEYWORD
| nonn,more
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AUTHOR
| Edwin Clark (eclark(AT)math.usf.edu) and Meeussen Wouter (wouter.meeussen(AT)pandora.be), Apr 29 2003
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EXTENSIONS
| Term 1212 added by Vladimir Reshetnikov, Oct 29 2011
a(1) added by Franklin T. Adams-Watters, Nov 03 2011
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