|
Search: id:A114506
|
|
|
| A114506 |
|
Triangle read by rows: T(n,k) is number of Dyck paths of semilength n having k ascents of length 3 (0<=k<=floor(n/3)). Also number of ordered trees with n edges that have k vertices of outdegree 3. |
|
+0
3
|
|
| 1, 1, 2, 4, 1, 10, 4, 27, 15, 79, 50, 3, 240, 168, 21, 750, 568, 112, 2387, 1959, 504, 12, 7711, 6850, 2115, 120, 25214, 24211, 8536, 825, 83315, 86164, 33858, 4620, 55, 277799, 308152, 133068, 23166, 715, 933596, 1106028, 520338, 108472, 6006
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
Row n has 1+floor(n/3) terms. Row sums yield the Catalan numbers (A000108). Column 0 yields A114507. Sum(kT(n,k),k=0..floor(n/3))=binomial(2n-4,n-3) (A001791).
|
|
FORMULA
|
G.f. G=G(t, z) satisfies (1-t)z^4*G^4-(1-t)z^3*G^3+zG^2-G+1=0.
|
|
EXAMPLE
|
T(4,1)=4 because we have UDUUUDDD, UUUDDDUD, UUUDUDDD and UUUDDUDD, where U=(1,1), D=(1,-1).
Triangle starts:
1;
1;
2;
4,1;
10,4;
27,15;
79,50,3;
240,168,21;
|
|
CROSSREFS
|
Cf. A000108, A001791, A114507, A102402, A114508.
Sequence in context: A116424 A135306 A102405 this_sequence A114848 A135330 A135328
Adjacent sequences: A114503 A114504 A114505 this_sequence A114507 A114508 A114509
|
|
KEYWORD
|
nonn,tabf
|
|
AUTHOR
|
Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 03 2005
|
|
|
Search completed in 0.002 seconds
|
