A001283 Triangle read by rows, in which row n consists of n(n+m) for m = 1 .. n-1.

6, 12, 15, 20, 24, 28, 30, 35, 40, 45, 42, 48, 54, 60, 66, 56, 63, 70, 77, 84, 91, 72, 80, 88, 96, 104, 112, 120, 90, 99, 108, 117, 126, 135, 144, 153, 110, 120, 130, 140, 150, 160, 170, 180, 190, 132, 143, 154, 165, 176, 187, 198, 209, 220, 231, 156, 168, 180

Offset: 2

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• tabl

Comments

With a different offset: triangle read by rows: t(n, m) = T(n+1, m) = (n+1)(n+m+1) = radius of C-excircle of Pythagorean triangle with sides a=(n+1)^2-m^2, b=2*(n+1)*m and c=(n+1)^2+m^2. - Floor van Lamoen, Aug 21 2001

Examples

			The triangle T(n, m) begins:
n\m   1   2   3   4   5   6   7   8   9  10  11  12  13  14 ...
2:    6
3:   12  15
4:   20  24  28
5:   30  35  40  45
6:   42  48  54  60  66
7:   56  63  70  77  84  91
8:   72  80  88  96 104 112 120
9:   90  99 108 117 126 135 144 153
10: 110 120 130 140 150 160 170 180 190
11: 132 143 154 165 176 187 198 209 220 231
12: 156 168 180 192 204 216 228 240 252 264 276
13: 182 195 208 221 234 247 260 273 286 299 312 325
14: 210 224 238 252 266 280 294 308 322 336 350 364 378
15: 240 255 270 285 300 315 330 345 360 375 390 405 420 435
...
[Reformatted and extended by _Wolfdieter Lang_, Dec 02 2014]
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Links

• T. D. Noe, Rows n = 2..100, flattened

Crossrefs

Cf. A003991, A063929, A063930.

Row sums are in A085788. Central column is A033581.

Programs

Mathematica

Flatten[Table[n*(n+m), {n, 2, 10}, {m, n-1}]] (* T. D. Noe, Jun 27 2012 *)

Formula

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

Extensions

Edited comment by Wolfdieter Lang, Dec 02 2014