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Search: id:A115590
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| A115590 |
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a(0) = 1; a(n+1) = (1+a(n))^3. |
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+0
1
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| 0, 1, 8, 729, 389017000, 58871587162270593034051001, 204040901322752673844230437877671861543858084850895762746141813554591014612008
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Take the rooted ternary tree of depth n, with (3^(n+1) - 1) / 2 labeled nodes. Let the number of rooted subtrees be a(n). For example, for n = 1 the a(2) = 8 subtrees are:
R...R...R...R......R.......R...R.......R
.../....|....\..../.\...../|...|\...../|\
..o.....o.....o..o...o...o.o...o.o...o.o.o
Then a(n+1) = (1+a(n))^3.
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REFERENCES
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A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fib. Quart., 11 (1973), 429-437.
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LINKS
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A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fib. Quart., 11 (1973), 429-437.
Index entries for sequences related to rooted trees
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FORMULA
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As for A004019, it follows from Aho and Sloane that there is a constant c such that a(n) is the nearest integer to c^(3^n). In fact a(n) = nearest integer to b^(3^n) - 1 where b = 2.0804006677503193521177452323719035237099784935372250879749088464344434056773788...
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CROSSREFS
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Cf. A004019.
Sequence in context: A017007 A023813 A068895 this_sequence A134923 A144230 A110039
Adjacent sequences: A115587 A115588 A115589 this_sequence A115591 A115592 A115593
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KEYWORD
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easy,nonn
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AUTHOR
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Paolo Bonzini (bonzini(AT)gnu.org), Mar 15 2006; corrected Apr 06 2006 and Jan 19 2007
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