A290451
Irregular triangle read by rows: row n (n>=1) lists the distinct areas of integer-sided triangles whose area equals n times their perimeter.
Original entry on oeis.org
24, 30, 36, 42, 60, 84, 96, 108, 120, 132, 144, 156, 168, 180, 240, 264, 300, 324, 396, 420, 684, 1224, 192, 204, 210, 216, 240, 252, 264, 270, 324, 330, 336, 378, 384, 408, 420, 456, 462, 480, 504, 522, 540, 546, 624, 690, 714, 780, 792, 840, 876, 966, 990, 1176, 1248, 1320, 1380, 1806, 2394, 2460, 3120, 4446, 8436, 336, 360, 384, 432, 456, 480, 528, 576, 624, 672, 720, 840, 960, 1056, 1176
Offset: 1
The first few rows of the triangle are:
(n=1) 24, 30, 36, 42, 60
(n=2) 84, 96, 108, 120, 132, 144, 156, 168, 180, 240, 264, 300, 324, 396, 420, 684, 1224
(n=3) 192, 204, 210, 216, 240, 252, 264, 270, 324, 330, 336, 378, ... (truncated)
(n=4) 336, 360, 384, 432, 456, 480, 528, 576, 624, 672, 720, 840, ... (truncated)
(n=5) 540, 600, 630, 660, 750, 810, 840, 900, 930, 1050, 1080, ... (truncated)
(n=6) 756, 768, 780, 816, 840, 864, 924, 960, 972, 984, 1008, ... (truncated)
(n=7) 1134, 1176, 1344, 1386, 1470, 1596, 1680, 1764, 1848, 1890, ... (truncated)
...
For the initial term in each row see
A289155, for last term see
A289156.
-
row[k_] := Block[{v={},r,s,t}, Do[If[r <= s && 4 k^2 < r s <= 12 k^2 && IntegerQ[ t = 4 k^2 (r + s)/(r s - 4 k^2)] && t >= s, AppendTo[v, r+s+t ]], {r, Floor[2 Sqrt[3] k]}, {s, Floor[4 k^2/r], Ceiling[12 k^2/r]}]; 2 k Union@ v]; Join @@ Array[row, 4] (* Giovanni Resta, Mar 04 2020 *)
Title modified and inconsistent double occurrence of 168 (a(14)) deleted by
Hugo Pfoertner, Mar 04 2020
A289253
Areas of integer-sided triangles whose area equals 7 times their perimeter.
Original entry on oeis.org
1134, 1176, 1344, 1386, 1470, 1596, 1680, 1764, 1848, 1890, 2016, 2058, 2184, 2310, 2394, 2520, 2604, 2856, 2940, 3024, 3360, 3696, 3780, 3864, 4032, 4242, 4368, 4536, 4830, 5292, 5544, 5712, 6006, 6090, 6216, 6258, 6510, 6636, 6720
Offset: 1
The areas 1134,1176,1344,1386,1470, ... pertain respectively to triangles with sides (39,60,63), (42,56,70), (40,68,84), (36,77,85), (35,84,91)...., equal 7 times their perimeter 162,168,192,198,210,...
Cf.
A332927 (listing distinct triangles with identical areas separately).
A332879
Areas of integer-sided triangles whose area equals 6 times their perimeter.
Original entry on oeis.org
756, 768, 780, 816, 840, 864, 924, 960, 972, 984, 1008, 1020, 1056, 1080, 1092, 1116, 1140, 1188, 1260, 1296, 1320, 1344, 1380, 1404, 1500, 1512, 1536, 1620, 1632, 1680, 1716, 1740, 1824, 1836, 1848, 1920, 1980, 2016, 2088, 2160, 2184, 2244, 2376, 2436, 2460
Offset: 1
Cf.
A332926 (listing distinct triangles with identical areas separately).
A332922
2*a(n) are the perimeters of distinct triangles with integer sides i <= j <= k, whose area equals 2 times their perimeter. Terms occurring more than once belong to different triangles.
Original entry on oeis.org
21, 24, 27, 30, 33, 36, 39, 42, 42, 45, 60, 66, 75, 81, 99, 105, 171, 306
Offset: 1
A332925
6*a(n) are the perimeters of distinct triangles with integer sides i <= j <= k, whose area equals 5 times their perimeter. Terms occurring more than once belong to different triangles.
Original entry on oeis.org
18, 20, 21, 22, 22, 25, 27, 28, 28, 30, 31, 35, 36, 44, 46, 50, 52, 53, 58, 68, 68, 69, 76, 77, 77, 84, 86, 99, 105, 108, 124, 134, 145, 151, 154, 182, 182, 209, 210, 242, 252, 260, 266, 391, 407, 468, 629, 742, 901, 910, 1751, 3434
Offset: 1
The 47 terms of
A289221, divided by 30, are all terms of this sequence, but omitting distinct triangles with identical perimeters.
Showing 1-5 of 5 results.
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