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A181944
Number of convex quadrilaterals, distinct up to congruence, on an n X n grid (or geoboard).
5
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
1,3
LINKS
Lucas A. Brown, Python program.
Eric Weisstein's World of Mathematics, Convex Polygon.
Eric Weisstein's World of Mathematics, Quadrilateral.
EXAMPLE
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 . |
+-------+-------+-------+-------+
CROSSREFS
Cf. A189413.
Sequence in context: A009657 A012088 A083825 * A359311 A193285 A199558
KEYWORD
nonn
AUTHOR
Martin Renner, Apr 03 2012
EXTENSIONS
a(7)-a(33) from Lucas A. Brown, Feb 06 2024
STATUS
approved