|
Search: id:A034929
|
|
|
| A034929 |
|
A triangle of Motzkin ballot numbers, read by rows. |
|
+0
2
|
|
| 1, 1, 1, 1, 2, 1, 1, 3, 3, 2, 1, 4, 6, 6, 4, 1, 5, 10, 13, 13, 9, 1, 6, 15, 24, 30, 30, 21, 1, 7, 21, 40, 59, 72, 72, 51, 1, 8, 28, 62, 105, 148, 178, 178, 127, 1, 9, 36, 91, 174, 276, 378, 450, 450, 323, 1, 10, 45, 128, 273, 480, 730, 980, 1158, 1158, 835, 1, 11, 55, 174, 410, 791
(list; table; graph; listen)
|
|
|
OFFSET
|
1,5
|
|
|
COMMENT
|
Mirror image of A091836. Row sums are the Motzkin numbers (A001006). T(n,n-1)=A001006(n-2) (the Motzkin numbers). T(n,n-2)=A005554(n-1).
|
|
REFERENCES
|
M. Aigner, Motzkin numbers, Europ. J. Comb. 19 (1998), 663-675.
|
|
FORMULA
|
G.f.= 2(1+tz)/[1-2z+tz-2tz^2+sqrt(1-2tz-3t^2*z^2)].
|
|
EXAMPLE
|
Triangle begins:
[1],
[1, 1],
[1, 2, 1],
[1, 3, 3, 2],
[1, 4, 6, 6, 4],
[1, 5, 10, 13, 13, 9],
[1, 6, 15, 24, 30, 30, 21],
[1, 7, 21, 40, 59, 72, 72, 51]
|
|
CROSSREFS
|
Cf. A001006, A091836, A005554.
Sequence in context: A010356 A100640 A144401 this_sequence A099509 A153859 A131336
Adjacent sequences: A034926 A034927 A034928 this_sequence A034930 A034931 A034932
|
|
KEYWORD
|
nonn,tabl
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com).
|
|
EXTENSIONS
|
Edited by Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 11 2004
|
|
|
Search completed in 0.002 seconds
|
