A007501 a(0) = 2; for n >= 0, a(n+1) = a(n)*(a(n)+1)/2.
2, 3, 6, 21, 231, 26796, 359026206, 64449908476890321, 2076895351339769460477611370186681, 2156747150208372213435450937462082366919951682912789656986079991221
Offset: 0
Examples
Example for depth 2 (the nonisomorphic possibilities are AAAA, AAAB, AABB, ABAB, ABBB, BBBB):
o
/ \
/ \
o o
/ \ / \
/ \ / \
A B B B
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]
- J.S. Seneschal, Iteration of Complete Graphs
- Stephan Wagner, Enumeration of highly balanced trees
Crossrefs
Programs
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Haskell
a007501 n = a007501_list !! n a007501_list = iterate a000217 2 -- Reinhard Zumkeller, Aug 15 2013
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Mathematica
f[n_Integer] := n(n + 1)/2; NestList[f, 2, 10]
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PARI
a(n)=if(n<1,2,a(n-1)*(1+a(n-1))/2)
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
a(n) = A145272(n) + a(n-1). - J.S. Seneschal, Jul 17 2025
Comments