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A217298 Triangle read by columns: T(n,k) = number of AVL trees of height n with k (leaf-) nodes, k>=1, A029837(k)<=n<A072649(k). 11
1, 1, 2, 1, 4, 6, 4, 1, 16, 32, 44, 60, 70, 56, 128, 28, 448, 8, 864, 1, 1552, 2720, 4288, 6312, 9004, 11992, 4096, 14372, 22528, 15400, 67584, 14630, 159744, 11968, 334080, 8104, 644992, 4376, 1195008, 1820, 2158912, 560, 3811904, 120, 6617184, 16, 11307904 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
REFERENCES
F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Camb. 1998, p. 239, Eq 79, A_5.
D. E. Knuth, Art of Computer Programming, Vol. 3, Sect. 6.2.3 (7) and (8).
LINKS
Ralf Hinze, Functional Pearls: Purely functional 1-2 brother trees, Journal of Functional Programming, 19(6):633-644, 2009, DOI: 10.1017/S0956796809007333.
R. C. Richards, Shape distribution of height-balanced trees, Info. Proc. Lett., 17 (1983), 17-20.
Wikipedia, AVL tree
EXAMPLE
There are 2 AVL trees of height 2 with 3 (leaf-) nodes:
o o
/ \ / \
o N N o
/ \ / \
N N N N
Triangle begins:
1
. 1
. . 2 1
. . . . 4 6 4 1
. . . . . . . 16 32 44 60 70 56 28 8 1
. . . . . . . . . . . . 128 448 864 1552 2720 ...
CROSSREFS
Triangle read by rows gives: A143897.
Row sums give: A029758.
Column sums give: A006265.
First elements of rows give: A174677.
First, last elements of columns give: A217299, A217300.
Row lengths give: 1+A008466(n).
Column heights give: A217710(k).
Sequence in context: A345135 A291057 A143897 * A217299 A333340 A217300
KEYWORD
nonn,look,tabf
AUTHOR
Alois P. Heinz, Mar 17 2013
STATUS
approved

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Last modified February 26 02:39 EST 2024. Contains 370335 sequences. (Running on oeis4.)