|
Search: id:A097891
|
|
|
| A097891 |
|
Triangle read by rows: T(n,k) is the number of Motzkin paths of length n and having k peaks at odd height. |
|
+0
1
|
|
| 1, 1, 1, 1, 2, 2, 5, 3, 1, 12, 6, 3, 28, 16, 6, 1, 66, 44, 13, 4, 159, 117, 36, 10, 1, 390, 308, 108, 24, 5, 969, 817, 317, 69, 15, 1, 2432, 2188, 912, 220, 40, 6, 6157, 5898, 2616, 698, 120, 21, 1, 15707, 15968, 7526, 2164, 401, 62, 7, 40340, 43381, 21696, 6638, 1355
(list; graph; listen)
|
|
|
OFFSET
|
0,5
|
|
|
COMMENT
|
Row sums are the Motzkin numbers (A001006).
|
|
FORMULA
|
G.f.=G=G(t, z) satisfies z^2*(1-z+z^2-tz^2)G^2-(1-z)(1-z+z^2-tz^2)G+1-z=0.
|
|
EXAMPLE
|
Triangle begins:
1;
1;
1,1;
2,2;
5,3,1;
12,6,3;
Row n has 1+floor(n/2) terms.
T(5,2)=3 counts H(UD)(UD), (UD)H(UD) and (UD)(UD)H, where U=(1,1), H=(1,0), D=(1,-1) (the peaks at odd height are shown between parentheses).
|
|
CROSSREFS
|
Cf. A001006.
Sequence in context: A114976 A085483 A038041 this_sequence A097611 A135376 A132850
Adjacent sequences: A097888 A097889 A097890 this_sequence A097892 A097893 A097894
|
|
KEYWORD
|
nonn,tabf
|
|
AUTHOR
|
Emeric Deutsch (deutsch(AT)duke.poly.edu), Sep 03 2004
|
|
|
Search completed in 0.002 seconds
|
