login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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