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

3,2

Comments

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

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).

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

Formula

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

Example

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

Crossrefs

Cf. A006600, A007678.

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

Sequence in context: A225610 A009921 A050188 * A038416 A217745 A213949

Adjacent sequences: A062358 A062359 A062360 * A062362 A062363 A062364

Keyword

easy,nonn

Author

Sascha Kurz, Jul 07 2001

Status

approved