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A290451
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Irregular triangle read by rows: row n (n>=1) lists the distinct areas of integer-sided triangles whose area equals n times their perimeter.
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10
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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
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OFFSET
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1,1
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COMMENTS
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Since the rows are long, more than the usual number of terms is shown. However, all rows are finite.
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LINKS
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EXAMPLE
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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)
...
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MATHEMATICA
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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 *)
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CROSSREFS
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For the initial term in each row see A289155, for last term see A289156.
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KEYWORD
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nonn,tabf
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AUTHOR
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EXTENSIONS
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Title modified and inconsistent double occurrence of 168 (a(14)) deleted by Hugo Pfoertner, Mar 04 2020
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STATUS
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approved
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