A340688 Irregular table read by rows: Take a concave circular triangle with all diagonals drawn, as in A340685. Then T(n,k) = number of k-sided polygons in that figure for k >= 3.
1, 12, 22, 3, 3, 66, 36, 67, 108, 12, 222, 186, 48, 6, 265, 465, 132, 6, 582, 786, 174, 48, 732, 1905, 324, 76, 3, 6, 1410, 2268, 558, 156, 6, 1704, 3732, 861, 223, 18, 3, 2778, 4242, 1260, 324, 42, 3369, 6540, 1872, 409, 42, 24, 4896, 7302, 2502, 540, 72, 24, 6138, 10467, 3306, 907, 99, 30
Offset: 1
Examples
A concave circular triangle with 1 point dividing its edges, n = 2, contains 12 triangles and no other n-gons, so the second row is [12]. A concave circular triangle with 2 points dividing its edges, n = 3, contains 22 triangles, 3 quadrilaterals, 3 pentagons and no other n-gons, so the third row is [22, 3, 3]. The table begins: 1; 12; 22, 3, 3; 66, 36; 67, 108, 12; 222, 186, 48, 6; 265, 465, 132, 6; 582, 786, 174, 48; 732, 1905, 324, 76, 3, 6; 1410, 2268, 558, 156, 6; 1704, 3732, 861, 223, 18, 3; 2778, 4242, 1260, 324, 42; 3369, 6540, 1872, 409, 42, 24; 4896, 7302, 2502, 540, 72, 24; 6138, 10467, 3306, 907, 99, 30; 8364, 12522, 4566, 1020, 120, 18; 10132, 16149, 5439, 1410, 288, 57, 0, 3; 13398, 19308, 6870, 1962, 252, 30, 12; 16029, 23082, 8859, 2422, 336, 90, 3; 20682, 29658, 10800, 2976, 528, 66;
Links
- Scott R. Shannon, Image of the regions for n = 20.
- Wikipedia, Circular triangle.
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