OFFSET
0,1
COMMENTS
Number of nonisomorphic complete binary trees with leaves colored using two colors. - Brendan McKay, Feb 01 2001
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
REFERENCES
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).
LINKS
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
FORMULA
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
EXAMPLE
Example for depth 2 (the nonisomorphic possibilites are AAAA, AAAB, AABB, ABAB, ABBB, BBBB):
.........o
......../.\
......./...\
......o.....o
...../.\.../.\
..../...\./...\
....A...B.B...B
MATHEMATICA
f[n_Integer] := n(n + 1)/2; NestList[f, 2, 10]
PROG
(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
CROSSREFS
Cf. A129440.
KEYWORD
nonn,easy
AUTHOR
STATUS
approved