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A007501
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a(0) = 2; for n >= 0, a(n+1) = a(n)*(a(n)+1)/2.
(Formerly M0818)
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35
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OFFSET
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0,1
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COMMENTS
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Number of nonisomorphic complete binary trees with leaves colored using two colors. - Brendan McKay, Feb 01 2001
a(0) = 2; for n>0, a(n) = A000217(a(n-1)). - Jonathan Vos Post, Nov 13 2004
With a(0) = 2, a(n+1) is the number of possible distinct sums between any number of elements in {1,...,a(n)}. - Derek Orr, Dec 13 2014
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REFERENCES
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W. H. Cutler, Subdividing a Box into Completely Incongruent Boxes, J. Rec. Math., 12 (1979), 104-111.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 0..12
G. L. Honaker, Jr., 41041 (another Prime Pages' Curiosity)
J. C. Kieffer, Hierarchical Type Classes and Their Entropy Functions, in 2011 First International Conference on Data Compression, Communications and Processing, pp. 246-254; Digital Object Identifier: 10.1109/CCP.2011.36.
J. V. Post, Math Pages [wayback copy]
Stephan Wagner, Enumeration of highly balanced trees
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FORMULA
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a(n) = A006893(n+1) + 1.
a(n+1) = A000217(a(n)). - Reinhard Zumkeller, Aug 15 2013
a(n) ~ 2 * c^(2^n), where c = 1.34576817070125852633753712522207761954658547520962441996... . - Vaclav Kotesovec, Dec 17 2014
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EXAMPLE
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Example for depth 2 (the nonisomorphic possibilites are AAAA, AAAB, AABB, ABAB, ABBB, BBBB):
.........o
......../.\
......./...\
......o.....o
...../.\.../.\
..../...\./...\
....A...B.B...B
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MATHEMATICA
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f[n_Integer] := n(n + 1)/2; NestList[f, 2, 10]
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PROG
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(PARI) a(n)=if(n<1, 2, a(n-1)*(1+a(n-1))/2)
(Haskell)
a007501 n = a007501_list !! n
a007501_list = iterate a000217 2 -- Reinhard Zumkeller, Aug 15 2013
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CROSSREFS
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Cf. A000217, A006893.
Cf. A117872 (parity), A275342 (2-adic valuation).
Cf. A129440.
Cf. A013589 (start=4), A050542 (start=5), A050548 (start=7), A050536 (start=8), A050909 (start=9).
Sequence in context: A024485 A013155 A303224 * A227367 A270397 A278106
Adjacent sequences: A007498 A007499 A007500 * A007502 A007503 A007504
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, Robert G. Wilson v
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STATUS
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approved
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