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A307681 Difference between the number of diagonals and the number of sides for a convex n-gon. 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

COMMENTS

The number of diagonals for a convex polygon with n sides is n*(n-3)/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*(n-5)/2.

CROSSREFS

Cf. A000096 (number of diagonals of an n-gon).

Cf. A006561 (number of intersections of diagonals in the interior of regular n-gon).

Cf. A007678 (number of regions in regular n-gon 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

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Last modified September 30 21:27 EDT 2020. Contains 337440 sequences. (Running on oeis4.)