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A371659
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Triangle read by rows: T(n,k) is the number of planar tanglegrams of size n with irreducible component of size k.
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0
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1, 0, 1, 0, 1, 1, 0, 3, 3, 5, 0, 13, 9, 20, 34, 0, 90, 46, 70, 170, 273, 0, 747, 312, 360, 680, 1638, 2436, 0, 7040, 2580, 2435, 3570, 7371, 17052, 23391, 0, 71736, 24056, 19800, 23970, 39858, 85260, 187128, 237090, 0, 774738, 243483, 182850, 193664, 267813, 477456, 1029204, 2133810, 2505228
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OFFSET
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1,8
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COMMENTS
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A proper subtanglegram of a planar tanglegram is a pair of subtrees whose leaves are matched in the tanglegram, and the irreducible component of a planar tanglegram is formed by contracting each maximal proper subtanglegram into a pair of matched leaves.
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LINKS
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FORMULA
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G.f.: F(x,y) = H(F(x),y) + x*y + y^2*(F(x)^2 + F(x^2))/2 where the coefficient of x^n*y^k is the number of planar tanglegrams of size n with irreducible component of size k, F(x) is the g.f. for A349408, and H(x)/x^2 is the g.f. for A257887.
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EXAMPLE
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Triangle begins
1;
0, 1;
0, 1, 1;
0, 3, 3, 5;
0, 13, 9, 20, 34;
0, 90, 46, 70, 170, 273;
0, 747, 312, 360, 680, 1638, 2436;
0, 7040, 2580, 2435, 3570, 7371, 17052, 23391;
...
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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