A007501 a(0) = 2; for n >= 0, a(n+1) = a(n)*(a(n)+1)/2. (Formerly M0818)

2, 3, 6, 21, 231, 26796, 359026206, 64449908476890321, 2076895351339769460477611370186681, 2156747150208372213435450937462082366919951682912789656986079991221

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. 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 * A369996 A227367 A270397

Adjacent sequences: A007498 A007499 A007500 * A007502 A007503 A007504

Keyword

nonn,easy

Author

N. J. A. Sloane, Robert G. Wilson v

Status

approved