A353451 - cp's OEIS frontend

A353451 T(n,m) is the number of non-congruent quadrilaterals with integer vertex coordinates (x1,1), (n,y2), (x3,m), (1,y4), 1 < x1, x3 < n, 1 < y2, y4 < m, m <= n, such that the 6 distances between the 4 vertices are distinct and (x3-x1)*(y4-y2) = 0, where T(n,m) is a triangle read by rows.

n	a(n)
3	0
4	0
5	0
6	0
7	2
8	0
9	1
10	6
11	6
12	4
13	1
14	8
15	10
16	19
17	12
18	4
19	15
20	20
21	39
22	48
23	40
24	4
25	16
26	25
27	41
28	52
29	89
30	47
31	10
32	30
33	39
34	66
35	86
36	135
37	144
38	105
39	10
40	31
41	41
42	75
43	91
44	140
45	142
46	212
47	106
48	18
49	49
50	67
51	107
52	134
53	203
54	220
55	308
56	319
57	214
58	18
59	49
60	67
61	109
62	144
63	210
64	227
65	325
66	334
67	458
68	228

[0, 0, 0, 0, 2, 0, 1, 6, 6, 4, 1, 8, 10, 19, 12, 4, 15, 20, 39, 48, 40, 4, 16, 25, 41, 52, 89, 47, 10, 30, 39, 66, 86, 135, 144, 105, 10, 31, 41, 75, 91, 140, 142, 212, 106, 18, 49, 67, 107, 134, 203, 220, 308, 319, 214, 18, 49, 67, 109, 144, 210, 227, 325, 334, 458, 228]

cp's OEIS Frontend

A353451 T(n,m) is the number of non-congruent quadrilaterals with integer vertex coordinates (x1,1), (n,y2), (x3,m), (1,y4), 1 < x1, x3 < n, 1 < y2, y4 < m, m <= n, such that the 6 distances between the 4 vertices are distinct and (x3-x1)*(y4-y2) = 0, where T(n,m) is a triangle read by rows.

Table of values

List of values

n	a(n)
3	0
4	0
5	0
6	0
7	2
8	0
9	1
10	6
11	6
12	4
13	1
14	8
15	10
16	19
17	12
18	4
19	15
20	20
21	39
22	48
23	40
24	4
25	16
26	25
27	41
28	52
29	89
30	47
31	10
32	30
33	39
34	66
35	86
36	135
37	144
38	105
39	10
40	31
41	41
42	75
43	91
44	140
45	142
46	212
47	106
48	18
49	49
50	67
51	107
52	134
53	203
54	220
55	308
56	319
57	214
58	18
59	49
60	67
61	109
62	144
63	210
64	227
65	325
66	334
67	458
68	228

n	a(n)
3	0
4	0
5	0
6	0
7	2
8	0
9	1
10	6
11	6
12	4
13	1
14	8
15	10
16	19
17	12
18	4
19	15
20	20
21	39
22	48
23	40
24	4
25	16
26	25
27	41
28	52
29	89
30	47
31	10
32	30
33	39
34	66
35	86
36	135
37	144
38	105
39	10
40	31
41	41
42	75
43	91
44	140
45	142
46	212
47	106
48	18
49	49
50	67
51	107
52	134
53	203
54	220
55	308
56	319
57	214
58	18
59	49
60	67
61	109
62	144
63	210
64	227
65	325
66	334
67	458
68	228

n	a(n)
3	0
4	0
5	0
6	0
7	2
8	0
9	1
10	6
11	6
12	4
13	1
14	8
15	10
16	19
17	12
18	4
19	15
20	20
21	39
22	48
23	40
24	4
25	16
26	25
27	41
28	52
29	89
30	47
31	10
32	30
33	39
34	66
35	86
36	135
37	144
38	105
39	10
40	31
41	41
42	75
43	91
44	140
45	142
46	212
47	106
48	18
49	49
50	67
51	107
52	134
53	203
54	220
55	308
56	319
57	214
58	18
59	49
60	67
61	109
62	144
63	210
64	227
65	325
66	334
67	458
68	228