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A159769 Number of n-leaf binary trees that do not contain (((()())())(()(()()))) as a subtree. 1
1, 1, 2, 5, 14, 41, 124, 384, 1212, 3885, 12614, 41400, 137132, 457841, 1539150, 5205612, 17700450, 60473476, 207491052, 714668954, 2470156910, 8564900629, 29783782326, 103846841946, 362970362118, 1271546963124, 4463801464608 (list; graph; refs; listen; history; internal format)
OFFSET

1,3

COMMENTS

By 'binary tree' we mean a rooted, ordered tree in which each vertex has either 0 or 2 children.

a(n) is also the number of Dyck words of semilength n-1 with no DDUUU.

LINKS

Eric S. Rowland, Pattern avoidance in binary trees.

FORMULA

Generating function f(x) satisfies (x-2) x f(x)^2 + (2 x^2 - 2 x + 1) f(x) + (x-1) x = 0

CROSSREFS

Sequence in context: A161898 A159770 A159773 * A159771 A159768 A128739

Adjacent sequences:  A159766 A159767 A159768 * A159770 A159771 A159772

KEYWORD

nonn

AUTHOR

Eric S Rowland (erowland(AT)math.rutgers.edu), Apr 23 2009

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Last modified February 14 22:11 EST 2012. Contains 205669 sequences.