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Triangle read by rows, in which row n consists of n(n+m) for m = 1 .. n-1.
6

%I #24 Feb 03 2022 00:32:10

%S 6,12,15,20,24,28,30,35,40,45,42,48,54,60,66,56,63,70,77,84,91,72,80,

%T 88,96,104,112,120,90,99,108,117,126,135,144,153,110,120,130,140,150,

%U 160,170,180,190,132,143,154,165,176,187,198,209,220,231,156,168,180

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

%C 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

%H T. D. Noe, <a href="/A001283/b001283.txt">Rows n = 2..100, flattened</a>

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

%e The triangle T(n, m) begins:

%e n\m 1 2 3 4 5 6 7 8 9 10 11 12 13 14 ...

%e 2: 6

%e 3: 12 15

%e 4: 20 24 28

%e 5: 30 35 40 45

%e 6: 42 48 54 60 66

%e 7: 56 63 70 77 84 91

%e 8: 72 80 88 96 104 112 120

%e 9: 90 99 108 117 126 135 144 153

%e 10: 110 120 130 140 150 160 170 180 190

%e 11: 132 143 154 165 176 187 198 209 220 231

%e 12: 156 168 180 192 204 216 228 240 252 264 276

%e 13: 182 195 208 221 234 247 260 273 286 299 312 325

%e 14: 210 224 238 252 266 280 294 308 322 336 350 364 378

%e 15: 240 255 270 285 300 315 330 345 360 375 390 405 420 435

%e ...

%e [Reformatted and extended by _Wolfdieter Lang_, Dec 02 2014]

%e ----------------------------------------------------------------

%t Flatten[Table[n*(n+m), {n, 2, 10}, {m, n-1}]] (* _T. D. Noe_, Jun 27 2012 *)

%Y Cf. A003991, A063929, A063930.

%Y Row sums are in A085788. Central column is A033581.

%K nonn,easy,tabl

%O 2,1

%A _N. J. A. Sloane_

%E Edited comment by _Wolfdieter Lang_, Dec 02 2014