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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A232435 Number T(n,k) of compositions of n with exactly k (possibly overlapping) occurrences of the consecutive pattern 111; triangle T(n,k), n>=0, 0<=k<=max(0,n-2), read by rows.

Table of values

n a(n)
0 1
1 1
2 2
3 3
4 1
5 7
6 0
7 1
8 13
9 2
10 0
11 1
12 24
13 5
14 2
15 0
16 1
17 46
18 11
19 4
20 2
21 0
22 1
23 89
24 21
25 11
26 4
27 2
28 0
29 1
30 170
31 45
32 23
33 11
34 4
35 2
36 0
37 1
38 324
39 99
40 47
41 23
42 12
43 4
44 2
45 0
46 1
47 618
48 209
49 102
50 52
51 23
52 13
53 4
54 2
55 0
56 1
57 1183
58 427
59 226
60 112
61 55
62 24
63 14
64 4
65 2
66 0
67 1
68 2260
69 883
70 479

List of values

[1, 1, 2, 3, 1, 7, 0, 1, 13, 2, 0, 1, 24, 5, 2, 0, 1, 46, 11, 4, 2, 0, 1, 89, 21, 11, 4, 2, 0, 1, 170, 45, 23, 11, 4, 2, 0, 1, 324, 99, 47, 23, 12, 4, 2, 0, 1, 618, 209, 102, 52, 23, 13, 4, 2, 0, 1, 1183, 427, 226, 112, 55, 24, 14, 4, 2, 0, 1, 2260, 883, 479]