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A007501 a(0) = 2; for n >= 0, a(n+1) = a(n)*(a(n)+1)/2.
(Formerly M0818)
34
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

Let {t(k)} be the triangular numbers (A000217). Then a(0) = 2; for n>0, a(n) = t(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.

J. V. Post, "Iterated Triangular Numbers", preprint.

J. V. Post, "Iterated Polygonal Numbers", preprint.

J. V. Post, "Triangular Carmichael Numbers: The First 22 Identified", preprint.

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

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. A129440.

Cf. A013589 (start=4), A050542 (start=5), A050548 (start=7), A050536 (start=8), A050909 (start=9).

Sequence in context: A012924 A024485 A013155 * 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 February 19 07:39 EST 2018. Contains 299330 sequences. (Running on oeis4.)