login
This site is supported by donations to The OEIS Foundation.

 

Logo

The OEIS is looking to hire part-time people to help edit core sequences, upload scanned documents, process citations, fix broken links, etc. - Neil Sloane, njasloane@gmail.com

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A214568 Triangle read by rows: T(n,k) is the number of rooted trees t with n vertices yielding k distinct rooted trees with n+1 vertices when a pendant edge is added to a vertex of t (1<=k<=n). 3
1, 0, 1, 0, 1, 1, 0, 1, 1, 2, 0, 1, 2, 3, 3, 0, 1, 1, 6, 6, 6, 0, 1, 3, 7, 11, 14, 12, 0, 1, 1, 11, 16, 29, 32, 25, 0, 1, 3, 11, 26, 46, 72, 75, 52, 0, 1, 2, 16, 27, 79, 122, 182, 177, 113, 0, 1, 3, 18, 42, 101, 217, 336, 457, 420, 247, 0, 1, 1, 20, 47, 149, 303, 621, 911, 1160, 1005, 548 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,10

COMMENTS

Row n contains n entries.

Sum(T(n,k), k=1..n) = A000081(n) = number of rooted trees with n vertices.

Sum(k*T(n,k), k=1..n) = A000107(n).

T(n,n) = A004111(n).

T(n,3) = A032741(n-1) = number of  proper divisors of n-1; if d is a proper divisor of n-1 (= number of edges), consider d identical rooted trees with (n-1)/d edges, root degree 1, height 2 and identify their roots.

The bivariate g.f. can be computed with eq. (4.2) of Harary-Robinson. - R. J. Mathar, Sep 16 2015

LINKS

Table of n, a(n) for n=1..78.

F. Harary, R. W. Robinson, Isomorphic factorizations VIII: bisectable trees, Combinatorica 4 (2) (1984) 169-179.

FORMULA

No formula available. Entries have been obtained by counting (using Maple) the rooted trees (identified by their Matula-Goebel numbers) with the required properties (using A061775 and A214567).

EXAMPLE

Triangle starts:

1;

0,1;

0,1,1;

0,1,1,2;

0,1,2,3,3;

0,1,1,6,6,6;

0,1,3,7,11,14,12;

0,1,1,11,16,29,32,25;

Row 4 is 0,1,1,2 because the four rooted trees with 4 vertices generate 2,3,4,and 4 rooted trees with 5 vertices.

CROSSREFS

Cf. A000081, A000107, A004111, A032741, A061775, A214567.

Sequence in context: A145201 A284265 A119464 * A107017 A201076 A201079

Adjacent sequences:  A214565 A214566 A214567 * A214569 A214570 A214571

KEYWORD

nonn,tabl,hard

AUTHOR

Emeric Deutsch, Jul 26 2012

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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified May 27 07:59 EDT 2017. Contains 287203 sequences.