|
| |
|
|
A036767
|
|
Number of rooted trees with a degree constraint.
|
|
1
| |
|
|
1, 1, 2, 5, 14, 42, 131, 421, 1385, 4642, 15795, 54418, 189454, 665471, 2355510, 8393461, 30084695, 108394449, 392356788, 1426137550, 5203211200, 19048447855, 69951072700, 257609070810, 951172531880, 3520465229446, 13058843476526
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| Empirical: number of Dyck n-paths avoiding UUUUUU (or DDDDDD). e.g. of the 132 Dyck 6-paths U^6D^6 contains UUUUUU so a(6)=131. [From David Scambler, Mar 24 2011]
|
|
|
REFERENCES
| L. Takacs, Enumeration of rooted trees and forests, Math. Scientist 18 (1993), 1-10, esp. Eq. (6).
|
|
|
LINKS
| Index entries for sequences related to rooted trees
Vladimir Kruchinin, Compositae and their properties , arXiv:1103.2582
|
|
|
FORMULA
| G.f. A(x) satisfies A(x)=1+sum(n=1..5, (x*A(x))^n) [From Vladimir Kruchinin, Feb 22 2011].
|
|
|
MAPLE
| r := 5; [ seq((1/n)*add( (-1)^j*binomial(n, j)*binomial(2*n-2-j*(r+1), n-1), j=0..floor((n-1)/(r+1))), n=1..30) ]; end;
|
|
|
PROG
| (PARI) a(n)=if(n<0, 0, polcoeff(serreverse(x/sum(k=0, 5, x^k)+O(x^(n+2))), n+1)) (from R. Stephan)
|
|
|
CROSSREFS
| Sequence in context: A196417 A054392 A006930 * A061922 A162746 A148329
Adjacent sequences: A036764 A036765 A036766 * A036768 A036769 A036770
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
| |
|
|
