

A062361


Number of triangular regions in regular ngon with all diagonals drawn.


19



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
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OFFSET

3,2


COMMENTS

Also the number of 3cycles and maximum cliques in the npolygon diagonal intersection graph.  Eric W. Weisstein, Mar 0809 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. 135156.
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, 135156 (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 (4cycles), A300553 (5cycles), A300554 (6cycles).
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



