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 A338707 Number of 3-linear trees on n nodes. 3
 0, 0, 0, 0, 0, 0, 0, 1, 5, 22, 74, 219, 576, 1394, 3150, 6733, 13744, 26969, 51185, 94323, 169453, 297533, 512006, 865050, 1437739, 2353756, 3801041, 6060918, 9552826, 14894428, 22991659, 35159606, 53299703, 80137271, 119563216, 177091225, 260504790, 380720841 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,9 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 on arXiv, arXiv:1901.08502 [math.CO], 2019-2020. See Tables 1 and 2 (but beware errors). FORMULA G.f.: x^3*(P(x)-1)*((P(x) - 1/(1-x))^2/(1-x)^2 + (P(x^2) - 1/(1-x^2))/(1-x^2))/2 where P(x) is the g.f. of A000041. - Andrew Howroyd, Dec 17 2020 PROG (PARI) seq(n)={my(p=1/(eta(x + O(x^(n-5))))); Vec(x^3*(p-1)*((p - 1/(1-x))^2/(1-x)^2 + (subst(p, x, x^2) - 1/(1-x^2))/(1-x^2))/2, -n)} \\ Andrew Howroyd, Dec 17 2020 CROSSREFS Cf. A000041, A130131, A338706. Sequence in context: A011846 A241694 A220733 * A058750 A058752 A234351 Adjacent sequences:  A338704 A338705 A338706 * A338708 A338709 A338710 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 23 23:05 EDT 2021. Contains 348217 sequences. (Running on oeis4.)