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A114576 Triangle read by rows: T(n,k) is number of Motzkin paths of length n having k UH's, where U=(1,1), H=(1,0) (0<=k<=floor(n/3)).

Table of values

n a(n)
0 1
1 1
2 2
3 3
4 1
5 6
6 3
7 11
8 10
9 23
10 26
11 2
12 47
13 70
14 10
15 102
16 176
17 45
18 221
19 449
20 160
21 5
22 493
23 1121
24 539
25 35
26 1105
27 2817
28 1680
29 196
30 2516
31 7031
32 5082
33 868
34 14
35 5763
36 17604
37 14856
38 3486
39 126
40 13328
41 43996
42 42660
43 12810
44 840
45 30995
46 110147
47 120338
48 44640
49 4410
50 42

List of values

[1, 1, 2, 3, 1, 6, 3, 11, 10, 23, 26, 2, 47, 70, 10, 102, 176, 45, 221, 449, 160, 5, 493, 1121, 539, 35, 1105, 2817, 1680, 196, 2516, 7031, 5082, 868, 14, 5763, 17604, 14856, 3486, 126, 13328, 43996, 42660, 12810, 840, 30995, 110147, 120338, 44640, 4410, 42]