A244215 - cp's OEIS frontend

A244215 a(0)=0, and for n>=1, if n is the k-th Catalan number (A000108(k)), a(n) = k, otherwise the difference of the indices of the two largest Catalan numbers whose sum is less than or equal to n: a(n) = A244160(n) - A244160(n-A081290(n)).

n	a(n)
0	0
1	1
2	2
3	1
4	0
5	3
6	2
7	1
8	1
9	1
10	0
11	0
12	0
13	0
14	4
15	3
16	2
17	2
18	2
19	1
20	1
21	1
22	1
23	1
24	1
25	1
26	1
27	1
28	0
29	0
30	0
31	0
32	0
33	0
34	0
35	0
36	0
37	0
38	0
39	0
40	0
41	0
42	5
43	4
44	3
45	3
46	3
47	2
48	2
49	2
50	2
51	2
52	2
53	2
54	2
55	2
56	1
57	1
58	1
59	1
60	1
61	1
62	1
63	1
64	1
65	1
66	1
67	1
68	1
69	1
70	1
71	1
72	1
73	1
74	1
75	1
76	1
77	1
78	1
79	1
80	1
81	1
82	1
83	1
84	0
85	0
86	0
87	0
88	0
89	0
90	0
91	0
92	0
93	0
94	0
95	0
96	0
97	0
98	0
99	0
100	0
101	0
102	0
103	0
104	0
105	0
106	0
107	0
108	0
109	0
110	0
111	0
112	0
113	0
114	0
115	0
116	0
117	0
118	0
119	0
120	0
121	0
122	0
123	0
124	0
125	0
126	0
127	0
128	0
129	0
130	0
131	0
132	6

[0, 1, 2, 1, 0, 3, 2, 1, 1, 1, 0, 0, 0, 0, 4, 3, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 4, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6]

cp's OEIS Frontend

A244215 a(0)=0, and for n>=1, if n is the k-th Catalan number (A000108(k)), a(n) = k, otherwise the difference of the indices of the two largest Catalan numbers whose sum is less than or equal to n: a(n) = A244160(n) - A244160(n-A081290(n)).

Table of values

List of values

n	a(n)
0	0
1	1
2	2
3	1
4	0
5	3
6	2
7	1
8	1
9	1
10	0
11	0
12	0
13	0
14	4
15	3
16	2
17	2
18	2
19	1
20	1
21	1
22	1
23	1
24	1
25	1
26	1
27	1
28	0
29	0
30	0
31	0
32	0
33	0
34	0
35	0
36	0
37	0
38	0
39	0
40	0
41	0
42	5
43	4
44	3
45	3
46	3
47	2
48	2
49	2
50	2
51	2
52	2
53	2
54	2
55	2
56	1
57	1
58	1
59	1
60	1
61	1
62	1
63	1
64	1
65	1
66	1
67	1
68	1
69	1
70	1
71	1
72	1
73	1
74	1
75	1
76	1
77	1
78	1
79	1
80	1
81	1
82	1
83	1
84	0
85	0
86	0
87	0
88	0
89	0
90	0
91	0
92	0
93	0
94	0
95	0
96	0
97	0
98	0
99	0
100	0
101	0
102	0
103	0
104	0
105	0
106	0
107	0
108	0
109	0
110	0
111	0
112	0
113	0
114	0
115	0
116	0
117	0
118	0
119	0
120	0
121	0
122	0
123	0
124	0
125	0
126	0
127	0
128	0
129	0
130	0
131	0
132	6

n	a(n)
0	0
1	1
2	2
3	1
4	0
5	3
6	2
7	1
8	1
9	1
10	0
11	0
12	0
13	0
14	4
15	3
16	2
17	2
18	2
19	1
20	1
21	1
22	1
23	1
24	1
25	1
26	1
27	1
28	0
29	0
30	0
31	0
32	0
33	0
34	0
35	0
36	0
37	0
38	0
39	0
40	0
41	0
42	5
43	4
44	3
45	3
46	3
47	2
48	2
49	2
50	2
51	2
52	2
53	2
54	2
55	2
56	1
57	1
58	1
59	1
60	1
61	1
62	1
63	1
64	1
65	1
66	1
67	1
68	1
69	1
70	1
71	1
72	1
73	1
74	1
75	1
76	1
77	1
78	1
79	1
80	1
81	1
82	1
83	1
84	0
85	0
86	0
87	0
88	0
89	0
90	0
91	0
92	0
93	0
94	0
95	0
96	0
97	0
98	0
99	0
100	0
101	0
102	0
103	0
104	0
105	0
106	0
107	0
108	0
109	0
110	0
111	0
112	0
113	0
114	0
115	0
116	0
117	0
118	0
119	0
120	0
121	0
122	0
123	0
124	0
125	0
126	0
127	0
128	0
129	0
130	0
131	0
132	6

n	a(n)
0	0
1	1
2	2
3	1
4	0
5	3
6	2
7	1
8	1
9	1
10	0
11	0
12	0
13	0
14	4
15	3
16	2
17	2
18	2
19	1
20	1
21	1
22	1
23	1
24	1
25	1
26	1
27	1
28	0
29	0
30	0
31	0
32	0
33	0
34	0
35	0
36	0
37	0
38	0
39	0
40	0
41	0
42	5
43	4
44	3
45	3
46	3
47	2
48	2
49	2
50	2
51	2
52	2
53	2
54	2
55	2
56	1
57	1
58	1
59	1
60	1
61	1
62	1
63	1
64	1
65	1
66	1
67	1
68	1
69	1
70	1
71	1
72	1
73	1
74	1
75	1
76	1
77	1
78	1
79	1
80	1
81	1
82	1
83	1
84	0
85	0
86	0
87	0
88	0
89	0
90	0
91	0
92	0
93	0
94	0
95	0
96	0
97	0
98	0
99	0
100	0
101	0
102	0
103	0
104	0
105	0
106	0
107	0
108	0
109	0
110	0
111	0
112	0
113	0
114	0
115	0
116	0
117	0
118	0
119	0
120	0
121	0
122	0
123	0
124	0
125	0
126	0
127	0
128	0
129	0
130	0
131	0
132	6