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A007501 a(0) = 2; for n >= 0, a(n+1) = a(n)*(a(n)+1)/2.
(Formerly M0818)
35
2, 3, 6, 21, 231, 26796, 359026206, 64449908476890321, 2076895351339769460477611370186681, 2156747150208372213435450937462082366919951682912789656986079991221 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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

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 * A227367 A270397 A278106

Adjacent sequences:  A007498 A007499 A007500 * A007502 A007503 A007504

KEYWORD

nonn,easy

AUTHOR

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

STATUS

approved

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Last modified October 2 14:56 EDT 2022. Contains 357226 sequences. (Running on oeis4.)