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 A338706 Number of 2-linear trees on n nodes. 4
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,7 COMMENTS 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 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..1000 Tanay Wakhare, Eric Wityk, and Charles R. Johnson, The proportion of trees that are linear, Discrete Mathematics, 343.10 (2020): 112008. Also arXiv:1901.08502v2. See Tables 1 and 2 (but beware errors). FORMULA 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 EXAMPLE The a(6) = 1 tree is:          o   o          |   |      o---o---o---o PROG (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 CROSSREFS Cf. A000041, A130131, A338707, A338708. Sequence in context: A033811 A062446 A053208 * A338710 A336516 A286209 Adjacent sequences:  A338703 A338704 A338705 * A338707 A338708 A338709 KEYWORD nonn AUTHOR N. J. A. Sloane, Nov 05 2020, using data supplied by Eric Wityk EXTENSIONS Terms a(31) and beyond from Andrew Howroyd, Dec 17 2020 STATUS approved

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Last modified October 18 13:28 EDT 2021. Contains 348067 sequences. (Running on oeis4.)