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EXAMPLE
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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;
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