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 A110316 a(n) is the number of different shapes of balanced binary trees with n nodes. The tree is balanced if the total number of nodes in the left and right branch of every node differ by at most one. 7
 1, 1, 2, 1, 4, 4, 4, 1, 8, 16, 32, 16, 32, 16, 8, 1, 16, 64, 256, 256, 1024, 1024, 1024, 256, 1024, 1024, 1024, 256, 256, 64, 16, 1, 32, 256, 2048, 4096, 32768, 65536, 131072, 65536, 524288, 1048576, 2097152, 1048576, 2097152, 1048576, 524288, 65536, 524288 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The value of a(n) is always a power of 2. REFERENCES S. Giraudo, Intervals of balanced binary trees in the Tamari lattice, Arxiv preprint arXiv:1107.3472, 2011 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..2047 FORMULA a(0) = a(1) = 1; a(2*n) = 2*a(n)*a(n-1); a(2*n+1) = a(n)*a(n). MAPLE a:= proc(n) option remember; local r; `if`(n<2, 1,       `if`(irem(n, 2, 'r')=0, 2*a(r)*a(r-1), a(r)^2))     end: seq(a(n), n=0..50);  # Alois P. Heinz, Apr 10 2013 PROG a(0) := 1; a(1) := 1; for n from 1 by 1 { a(2*n) := 2*a(n)*a(n-1); a(2*n+1) := a(n)*a(n)} CROSSREFS Column k=2 of A221857. - Alois P. Heinz, Apr 17 2013 Sequence in context: A091335 A140946 A008741 * A111975 A117250 A136692 Adjacent sequences:  A110313 A110314 A110315 * A110317 A110318 A110319 KEYWORD easy,nonn AUTHOR Jeffrey A. Barnett (jbb(AT)notatt.com), Jun 23 2007 STATUS approved

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