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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 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: A024485 A013155 A303224 * A227367 A270397 A278106 Adjacent sequences:  A007498 A007499 A007500 * A007502 A007503 A007504 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified April 12 12:39 EDT 2021. Contains 342920 sequences. (Running on oeis4.)