A062361 Number of triangular regions in regular n-gon with all diagonals drawn.

1, 4, 10, 18, 35, 56, 90, 120, 176, 276, 377, 476, 585, 848, 1054, 1404, 1653, 2200, 2268, 2992, 3749, 4416, 5000, 6292, 6777, 8316, 9222, 11670, 11501, 14368, 15840, 18598, 19705, 24444, 25012, 28842, 30966, 36000, 39278, 45318, 46999, 53900

Offset: 3

Author

Sascha Kurz, Jul 07 2001

Keywords

• easy
• nonn

Comments

Also the number of 3-cycles and maximum cliques in the n-polygon diagonal intersection graph. - Eric W. Weisstein, Mar 08-09 2018

Examples

			a(4) = 4 because in a quadrilateral the diagonals cross to make four triangles.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 3..100
• B. Poonen and M. Rubinstein, Number of Intersection Points Made by the Diagonals of a Regular Polygon, SIAM J. Discrete Mathematics, Vol. 11, pp. 135-156.
• B. Poonen and M. Rubinstein, The number of intersection points made by the diagonals of a regular polygon, SIAM J. on Discrete Mathematics, Vol. 11, No. 1, 135-156 (1998).
• N. J. A. Sloane, Summary table for vertices and regions in regular n-gon with all chords drawn, for n = 3..19. [V = total number of vertices (A007569), V_i (i>=2) = number of vertices where i lines cross (A292105, A292104, A101363); R = total number of cells or regions (A007678), R_i (i>=3) = number of regions with i edges (A331450, A062361, A067151).]
• S. E. Sommars and T. Sommars, Number of Triangles Formed by Intersecting Diagonals of a Regular Polygon, J. Integer Sequences, 1 (1998), #98.1.5.
• Eric Weisstein's World of Mathematics, Graph Cycle
• Eric Weisstein's World of Mathematics, Maximum Clique
• Eric Weisstein's World of Mathematics, Polygon Diagonal Intersection Graph
• Sequences formed by drawing all diagonals in regular polygon

Crossrefs

Cf. A006600, A007678.

Cf. A300552 (4-cycles), A300553 (5-cycles), A300554 (6-cycles).

Formula

a(n) = n * A067162(n).