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A059283 Triangle T(n,k) (0<= k <=n) read by rows. Left edge is 1, 0, 0, ... Otherwise each entry is sum of entry to left, entries immediately above it to left and right and entry directly above it 2 rows back.

Table of values

n a(n)
0 1
1 0
2 1
3 0
4 2
5 3
6 0
7 2
8 8
9 11
10 0
11 2
12 14
13 36
14 47
15 0
16 2
17 20
18 78
19 172
20 219
21 0
22 2
23 26
24 138
25 424
26 862
27 1081
28 0
29 2
30 32
31 216
32 856
33 2314
34 4476
35 5557
36 0
37 2
38 38
39 312
40 1522
41 5116
42 12768
43 23882
44 29439
45 0
46 2
47 44
48 426
49 2476
50 9970
51 30168
52 71294
53 130172
54 159611
55 0
56 2
57 50
58 558

List of values

[1, 0, 1, 0, 2, 3, 0, 2, 8, 11, 0, 2, 14, 36, 47, 0, 2, 20, 78, 172, 219, 0, 2, 26, 138, 424, 862, 1081, 0, 2, 32, 216, 856, 2314, 4476, 5557, 0, 2, 38, 312, 1522, 5116, 12768, 23882, 29439, 0, 2, 44, 426, 2476, 9970, 30168, 71294, 130172, 159611, 0, 2, 50, 558]