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A115590
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a(0) = 0; a(n) = (1+a(n-1))^3 for n > 0.
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3
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OFFSET
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0,3
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COMMENTS
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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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LINKS
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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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MATHEMATICA
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{0}~Join~RecurrenceTable[{a[n]==(a[n-1]+1)^3, a[0]==1}, a, {n, 0, 8}] (* Vaclav Kotesovec, May 21 2015 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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Paolo Bonzini, Mar 15 2006; corrected Apr 06 2006 and Jan 19 2007
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EXTENSIONS
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STATUS
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approved
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