A063930 Radius of B-excircle of Pythagorean triangle with a=(n+1)^2-m^2, b=2*(n+1)*m and c=(n+1)^2+m^2.

3, 4, 10, 5, 12, 21, 6, 14, 24, 36, 7, 16, 27, 40, 55, 8, 18, 30, 44, 60, 78, 9, 20, 33, 48, 65, 84, 105, 10, 22, 36, 52, 70, 90, 112, 136, 11, 24, 39, 56, 75, 96, 119, 144, 171, 12, 26, 42, 60, 80, 102, 126, 152, 180, 210, 13, 28, 45, 64, 85, 108, 133, 160, 189, 220

Offset: 1

Author

Floor van Lamoen, Aug 21 2001

Keywords

• easy
• nonn
• tabl

Comments

See a comment for excircle and exradius on A063929, also for links.

Examples

			The triangle T(n, m) begins:
n\m  1  2  3  4   5   6   7   8   9  10  11  12  13  14  15 ...
1:   3
2:   4 10
3:   5 12 21
4:   6 14 24 36
5:   7 16 27 40  55
6:   8 18 30 44  60  78
7:   9 20 33 48  65  84 105
8:  10 22 36 52  70  90 112 136
9:  11 24 39 56  75  96 119 144 171
10: 12 26 42 60  80 102 126 152 180 210
11: 13 28 45 64  85 108 133 160 189 220 253
12: 14 30 48 68  90 114 140 168 198 230 264 300
13: 15 32 51 72  95 120 147 176 207 240 275 312 351
14: 16 34 54 76 100 126 154 184 216 250 286 324 364 406
15: 17 36 57 80 105 132 161 192 225 260 297 336 377 420 465
...
[Formatted and extended by _Wolfdieter Lang_, Dec 02 2014]
		

Crossrefs

Cf. A003991 (inradius), A063929 (A-exradius), A001283 (C-exradius), A055096 (circumradius diameter).

Formula

T(n,m) = m(n+m+1), n >= m >= 1.

T(n,m) = sqrt(s*(s-a)*(s-c)/(s-b)) with the semiperimeter s = (a + b + c)/2, and the a, b and c values given in the name substituted. - Wolfdieter Lang, Dec 02 2014

Extensions

Crossreferences commented and A055096 added by Wolfdieter Lang, Dec 02 2014