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 A346446 Irregular triangle read by rows: T(n,k) = number of k-sided polygons formed when connecting infinite lines between all vertices and all points that divide the sides of an equilateral triangle into n equal parts, for k = 3, 4, ..., max_k. 5
 1, 12, 75, 24, 3, 258, 132, 6, 621, 525, 33, 19, 1308, 1272, 144, 24, 2505, 2628, 345, 61, 4434, 4734, 984, 102, 12, 6, 7365, 7992, 1347, 243, 30, 9, 11556, 12552, 2412, 366, 48, 17073, 19266, 3969, 804, 60, 3, 0, 3, 0, 1, 24786, 27672, 6954, 1206, 186, 34611, 39066, 9099, 1768, 198, 27 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS See A344279 for other images of the polygons. LINKS Table of n, a(n) for n=1..58. Scott R. Shannon, Image of the k-gons for n=3. FORMULA Sum of row(n) = A344279(n) = A344896(n) - A344657(n) + 1. EXAMPLE Connecting infinite lines between an equilateral triangle's three vertices and the two points along each side that divide the sides into three equal parts forms seventy-five triangles, twenty-four quadrilaterals and three pentagons, so row 3 is [75,24,3]. See the linked image. The table begins: 1; 12; 75, 24, 3; 258, 132, 6; 621, 525, 33, 19; 1308, 1272, 144, 24; 2505, 2628, 345, 61; 4434, 4734, 984, 102, 12, 6; 7365, 7992, 1347, 243, 30, 9; 11556, 12552, 2412, 366, 48; 17073, 19266, 3969, 804, 60, 3, 0, 3, 0, 1; 24786, 27672, 6954, 1206, 186; 34611, 39066, 9099, 1768, 198, 27; 47028, 53688, 15318, 2676, 288, 24; 63039, 72210, 18513, 3708, 396, 75, 0, 6; 82746, 93570, 24930, 4536, 498, 54, 18; 106536, 121080, 32988, 6622, 678, 117, 6, 3; 134520, 155748, 46326, 9456, 1266, 102, 12; 167895, 196179, 55527, 11410, 1638, 156, 12, 3; 207294, 243294, 74796, 15396, 2106, 276, 42, 6; 254034, 297069, 87648, 17715, 2388, 363, 18, 3; 308022, 360228, 108264, 21858, 3090, 282, 42, 18; 370818, 433902, 132651, 28210, 4311, 486, 42, 9; 440952, 520044, 168156, 36228, 5484, 720, 78; 521031, 614526, 189297, 39541, 5790, 780, 60, 15; 612990, 723228, 232980, 49278, 8004, 822, 96; CROSSREFS Cf. A344279 (number of polygons), A344657 (number of vertices), A344896 (number of edges), A343755 (number of regions), A092867 (number polygons inside the triangle). Sequence in context: A156196 A041270 A055912 * A064121 A064116 A003368 Adjacent sequences: A346443 A346444 A346445 * A346447 A346448 A346449 KEYWORD nonn,tabf AUTHOR Scott R. Shannon, Jul 18 2021 STATUS approved

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Last modified June 8 11:34 EDT 2023. Contains 363164 sequences. (Running on oeis4.)