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A338706
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Number of 2-linear trees on n nodes.
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4
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0, 0, 0, 0, 0, 1, 3, 10, 24, 56, 114, 224, 411, 733, 1252, 2091, 3393, 5408, 8440, 12982, 19650, 29388, 43394, 63430, 91754, 131584, 187057, 263932, 369624, 514253, 710838, 976876, 1334828, 1814492, 2454011, 3303436, 4426627, 5906599, 7848883, 10389557
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OFFSET
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1,7
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COMMENTS
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A k-linear tree is a tree with exactly k vertices of degree 3 or higher all of which lie on a path. - Andrew Howroyd, Dec 17 2020
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LINKS
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FORMULA
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G.f.: ((x*(P(x) - 1/(1-x)))^2 + x^2*(P(x^2) - 1/(1-x^2)))/(2*(1-x)) where P(x) is the g.f. of A000041. - Andrew Howroyd, Dec 17 2020
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EXAMPLE
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The a(6) = 1 tree is:
o o
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o---o---o---o
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PROG
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(PARI) seq(n)=my(p=1/(eta(x + O(x^(n-3))))); Vec(((x*(p - 1/(1-x)))^2 + x^2*(subst(p, x, x^2) - 1/(1-x^2)))/(2*(1-x)), -n) \\ Andrew Howroyd, Dec 17 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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