A181945 Number of trapezoids, distinct up to congruence, on an n X n grid (or geoboard).

0, 1, 9, 43, 141, 343, 766, 1415, 2517, 4129, 6545, 9505, 14230, 19444, 26733, 36208, 48029, 60675, 78729, 96866, 122433, 151288, 184072, 217998, 266775, 315096, 371138, 435153, 512549, 585240, 688470, 779196, 895058, 1019697, 1153081, 1305629, 1494185, 1656287

Offset: 1

Author

Martin Renner, Apr 03 2012

Keywords

• nonn

Examples

			a(1) = 0 because the 1 X 1 grid has no trapezoids.
a(2) = 1 because the 2 X 2 grid has one trapezoid.
a(3) = 9 because the 3 X 3 grid has 9 congruence classes of trapezoids, out of 50 trapezoids 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 . |
+-------+-------+-------+
		

Links

• Lucas A. Brown, Python program.
• Eric Weisstein's World of Mathematics, Trapezoid.

Crossrefs

Cf. A181944, A189415.

Extensions

a(7)-a(38) from Lucas A. Brown, Feb 05 2024