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A159769
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Number of n-leaf binary trees that do not contain (((()())())(()(()()))) as a subtree.
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1
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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
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OFFSET
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1,3
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COMMENTS
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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.
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LINKS
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FORMULA
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G.f. f(x) satisfies (x-2) x f(x)^2 + (2 x^2 - 2 x + 1) f(x) + (x-1) x = 0.
Conjecture: 2*(n+1)*a(n) +3*(-3*n+1)*a(n-1) +2*(2*n-1)*a(n-2) +4*(2*n-7)*a(n-3) +2*(-2*n+7)*a(n-4)=0. - R. J. Mathar, May 30 2014
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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