

A307681


Difference between the number of diagonals and the number of sides for a convex ngon.


0



3, 2, 0, 3, 7, 12, 18, 25, 33, 42, 52, 63, 75, 88, 102, 117, 133, 150, 168, 187, 207, 228, 250, 273, 297, 322, 348, 375, 403, 432, 462, 493, 525, 558, 592, 627, 663, 700, 738, 777, 817, 858, 900, 943, 987, 1032, 1078, 1125, 1173, 1222, 1272, 1323, 1375, 1428, 1482, 1537, 1593, 1650, 1708, 1767, 1827, 1888, 1950, 2013, 2077, 2142, 2208, 2275
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OFFSET

3,1


COMMENTS

The number of diagonals for a convex polygon with n sides is n*(n3)/2.
For a triangle and a quadrilateral, the number of sides is greater than the number of diagonals. For a pentagon, the number of sides is equal to the number of diagonals. For an hexagon or a polygon with more than six sides, the number of diagonals is greater than the number of sides.


LINKS

Table of n, a(n) for n=3..70.
Ask Dr. Math, Polygon diagonals
Eric Weisstein's World of Mathematics, Polygon
Eric Weisstein's World of Mathematics, Polygon diagonal


FORMULA

a(n) = n*(n5)/2.


CROSSREFS

Cf. A000096 (number of diagonals of an ngon).
Cf. A006561 (number of intersections of diagonals in the interior of regular ngon).
Cf. A007678 (number of regions in regular ngon with all diagonals drawn).
Sequence in context: A231132 A290327 A131732 * A331922 A198826 A088161
Adjacent sequences: A307678 A307679 A307680 * A307682 A307683 A307684


KEYWORD

sign,easy


AUTHOR

Bernard Schott, Apr 21 2019


STATUS

approved



