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 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. 9
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Since the rows are long, more than the usual number of terms is shown. However, all rows are finite. LINKS EXAMPLE 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) ... MATHEMATICA 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 *) CROSSREFS For the initial term in each row see A289155, for last term see A289156. Rows are: n=1: A098030, n=2: A289218, n=3: A289219, n=4: A289220, n=5: A289221, n=6: A332879, n=7: A289253. Cf. A332689 (row lengths). Sequence in context: A075422 A230195 A098030 * A068544 A284174 A292982 Adjacent sequences:  A290448 A290449 A290450 * A290452 A290453 A290454 KEYWORD nonn,tabf AUTHOR N. J. A. Sloane, Aug 06 2017 EXTENSIONS Title modified and inconsistent double occurrence of 168 (a(14)) deleted by Hugo Pfoertner, Mar 04 2020 STATUS approved

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Last modified April 12 10:06 EDT 2021. Contains 342920 sequences. (Running on oeis4.)