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 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. 5
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS See A340685 for images of the regions and A340686 for images of the vertices. LINKS Table of n, a(n) for n=1..62. Scott R. Shannon, Image of the regions for n = 20. Wikipedia, Circular triangle. EXAMPLE 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; CROSSREFS Cf. A340685 (regions), A340686 (vertices), A340687 (edges), A340614, A007678, A092867. Sequence in context: A323084 A323083 A212958 * A031186 A078538 A278030 Adjacent sequences: A340685 A340686 A340687 * A340689 A340690 A340691 KEYWORD nonn,tabf AUTHOR Scott R. Shannon and N. J. A. Sloane, Jan 16 2021 STATUS approved

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Last modified July 14 05:06 EDT 2024. Contains 374291 sequences. (Running on oeis4.)