Integer diagonal of cuboid

Cuboid diagonal whose dimensions are: Height H x Breadth B x Length L
A typical case for having integer length of diagonal.
H	B	L
a	a+1	a(a+1)	a^2	(a+1)^2	a(a+1)^2	Diagonal ^2 of cuboid	Diagonal	[a(a+1)) +1]
1	2	2	1	4	4	9	3	3
2	3	6	4	9	36	49	7	7
3	4	12	9	16	144	169	13	13
4	5	20	16	25	400	441	21	21
5	6	30	25	36	900	961	31	31
6	7	42	36	49	1764	1849	43	43
7	8	56	49	64	3136	3249	57	57
8	9	72	64	81	5184	5329	73	73
9	10	90	81	100	8100	8281	91	91
10	11	110	100	121	12100	12321	111	111
11	12	132	121	144	17424	17689	133	133
12	13	156	144	169	24336	24649	157	157
13	14	182	169	196	33124	33489	183	183
14	15	210	196	225	44100	44521	211	211