A181944 Number of convex quadrilaterals, distinct up to congruence, on an n X n grid (or geoboard).

0, 1, 12, 89, 407, 1413, 3894, 9431, 20212, 39847, 73177, 127582, 211012, 337186, 519594, 777447, 1134269, 1620415, 2264873, 3114709, 4209184, 5609209, 7378581, 9594611, 12326333, 15688198, 19779188, 24721601, 30646522, 37727553, 46093734, 55983150, 67558997

Offset: 1

Author

Martin Renner, Apr 03 2012

Keywords

• nonn

Examples

			a(1) = 0 because the 1 X 1 grid has no quadrilaterals.
a(2) = 1 because the 2 X 2 grid has one quadrilateral.
a(3) = 9 because the 3 X 3 grid has 12 congruence classes of quadrilaterals, out of 70 quadrilaterals total:
+-------+-------+-------+-------+
| . . . | . o . | . . . | . o . |
| o o . | o . . | o . o | o . . |
| o o . | o o . | o . o | o . o |
+-------+-------+-------+-------+
| . . o | o . o | . o . | . o . |
| o . . | . . . | o o . | o . o |
| o . o | o . o | o . . | o . . |
+-------+-------+-------+-------+
| . o o | . . o | . o . | . . o |
| o . . | o . o | o . o | o . . |
| o . . | o . . | . o . | o o . |
+-------+-------+-------+-------+
		

Links

• Lucas A. Brown, Python program.
• Eric Weisstein's World of Mathematics, Convex Polygon.
• Eric Weisstein's World of Mathematics, Quadrilateral.

Crossrefs

Cf. A189413.

Extensions

a(7)-a(33) from Lucas A. Brown, Feb 06 2024