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A007501
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a(0) = 2; for n >= 0, a(n+1) = a(n)*(a(n)+1)/2.
(Formerly M0818)
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19
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2, 3, 6, 21, 231, 26796, 359026206, 64449908476890321, 2076895351339769460477611370186681, 2156747150208372213435450937462082366919951682912789656986079991221
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Number of nonisomorphic complete binary trees with leaves colored using two colors - Brendan McKay (bdm(AT)cs.anu.edu.au), Feb 01, 2001
Let {t(k)} be the triangular numbers (A000219). Then a(0) = 2; for n>0, a(n) = t(a(n-1)). - Jonathan Vos Post (jvospost3(AT)gmail.com), Nov 13 2004
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REFERENCES
| W. H. Cutler, Subdividing a Box into Completely Incongruent Boxes, J. Rec. Math., 12 (1979), 104-111.
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, "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).
STEPHAN WAGNER, ENUMERATION OF HIGHLY BALANCED TREES, http://www.cs.sun.ac.za/~swagner/balanced.pdF
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LINKS
| G. L. Honaker, Jr., 41041 (another Prime Pages' Curiosity)
J. V. Post, Math Pages
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EXAMPLE
| Example for depth 2 (the nonisomorpic possibilites are AAAA, AAAB, AABB, ABAB, ABBB, BBBB):
.........o
......../.\
......./...\
......o.....o
...../.\.../.\
..../...\./...\
....A...B.B...B
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MATHEMATICA
| f[n_Integer] := n(n + 1)/2; NestList[f, 2, 10]
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PROG
| (PARI) a(n)=if(n<1, 2, a(n-1)*(1+a(n-1))/2)
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CROSSREFS
| Equals A006893(n+1) + 1. Cf. A000217.
Cf. A129440.
Sequence in context: A012924 A024485 A013155 * A015773 A015768 A094470
Adjacent sequences: A007498 A007499 A007500 * A007502 A007503 A007504
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com)
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